The first thing to be said is that you should be suspicious of criticisms that can't point to a particular error, but just cast a vague negative stereotype over vast swaths of Catholic theology without actually engaging any of it. Granted, it's true in some sense, as you say, that saints and not scholars make the best theologians, but it's also true that a great many saints have written like and have even been scholars, and that a huge number of great saints, even when they have not themselves been scholars, have recommended scholarly theology as being a reliable tool for edification and personal sanctification. You will hear many people criticize St. Alphonsus Liguori, St. Thomas, St. Robert Bellarmine, St. Albert, St. Francis de Sales, (all doctors of the Church) and the members of their schools, but the people who do so never seem to be very interested in studying them or to have the humility and docility necessary to benefit from their thought.
I've heard many times the ridiculous accusation against St. Thomas that he is a rationalist. This is utterly absurd, as any decent reading of even a tiny fraction of the Prima Pars would reveal. The truth is that the Scholastics were interested in two things which the new theologians don't have much concern for: clarity and truth. In my experience, much of the new theology is focused on poetic richness instead of clarity, and "authentic" reflection instead of truth. It would seem to count more as "good theology" to a modern theologian if someone wrote a very vague poem about the Godhead capable of any number of controversial and heretical interpretations, than if they attempted in a rigorous and straightforward fashion to settle some modest question about the nature of the Divine Essence as revealed through Scripture. Modern theology is re-conceived as poetic experiential massage, instead of the clarification of articles of faith.
I'm going to skip railing against the nostalgia for the East and the absurdities of the Trinitarian theology you're reading, and talk a little bit about the problems with the New Theology and Resourcement generally. As a note, if you want a history of Vatican II, I highly recommend Roberto de Mattei's Vatican II: An Unwritten Story. It's very well-documented and was praised by Cardinal Brandmüller, who used to be head of the Pontifical Committee for Historical Sciences. I found it personally riveting and extremely illuminating. Additionally, you ought to read Pope Pius X's encyclical Pascendi Dominici Gregis if you haven't already.
One of the chief difficulties today is that because of the sudden and catastrophic loss of Latin fluency among students of theology, the majority of the Catholic theological tradition has effectively been lost overnight. What's left is for those who have the credentials and the gall to do so to make sweeping claims about the theological literature of the past 1500 years, so as to convince everyone else that (1) it is bad, theologically speaking, (2) it is intellectually stifling, (3) we must break from it, and be glad to have been rid of it. Who are these people, and why are they suddenly so intent on upending and "liberating" us from so many centuries of theological reflection?
The New Theology can be divided into two schools: Ressourcement and Aggiornamento. The former is based on the notion that scholastic metaphysics and the disputative/tractative style of theological exposition are contrary to the richness and depth which belonged to theology prior to the emergence of the Schools in the high middle ages. Patristic and Monastic theological reflection are ordered primarily toward the spiritual benefit of readers and listeners, and employ as their main form the exposition of scriptural texts. During the middle ages the habits of exegesis and spiritual care were (supposedly) abandoned by the main figures of scholastic theology, and replaced by an extremely dry and overly-technical sifting operation of no benefit to anyone outside of university faculties. The story goes that, as time went on, the scholastic theological systems became so refined, and reached down to such careful qualifications and distinctions, that the student of the Catholic Faith who desired to return to the sources of the tradition could no longer do so without being encumbered at every turn by the stifling jargon and nitpicking of baroque neo-scholastics. Where were these articles, tracts, and dubia in the homilies of Chrysostom? Doesn't Nazianzen himself mock the theologians who thrive on subtle distinctions? Isn't theology the work of the soul seeking perfection? With indignation, the Ressourcement theologians want to turn back to the days of the Fathers, when one didn't need to worry about some neo-scholastic manualist breathing down your neck because of a vague or infelicitous phrase. They want to set forth the faith with the newness of the kerygma present in the Greek Fathers, and to throw away all the trappings of suffocating rationalism that have burdened western theology for the past millennium.
There are several problems with this story. First, when one reads the Fathers, one has a definite sense that they are not only not averse to the use of philosophical tools in theological reflection, but that they often struggle to develop them as a means of clarifying and exposing the faith, and combating heresy. One finds even in the Greek Fathers early exercises in the systematic meeting of objections (cf. Justin Martyr) and systematic theological exposition (cf. John Damascene).
Second, the standard portrait of changes in medieval theology is completely wrong. The scholastic handbooks and Summae were developed as tools for pastors on the ground, to help them understand the mechanics of the faith and respond readily to spiritual doubts and moral quandaries. If one wants to help a parishioner deal with some spiritual question or difficulty, the works of St. Alphonsus and St. Thomas are going to be infinitely more useful than any text by Rahner, de Lubac, or Balthasar. The work of the scholastics was not to subordinate revealed truth to an artificial paradigm or intellectual system, but to organize and respond to common questions concerning what has been revealed so as to make the task of teaching, advising, and correcting simpler for those charged with it.
Third, if the task of theological reflection is more "stifling" now than it was a millennium ago, this is in large part because of the clarity that has resulted from the development of the doctrine of the faith. Where there were implicit material heresies in some of the Fathers, today we know how to eschew the offending language. Where there were theological missteps in some of the early scholastics, today we can correct for their misplaced metaphysical assumptions or ignorance of the tradition. These developments are advantages for those seeking to teach the faith, because we can do so, if we try, with less fear of error or confusion. To want to be free of the constraints suggested by the scholastics is to desire to be liberated from the logic of Divine Revelation itself—this is prideful and tends toward heresy.
Fourth, the tradition of scholastic theology between Gregory VII and Pius XII abandoned neither the composition of exegetical tracts and homilies on scripture, nor the practical application of theological insights to spiritual counsel. In the words of one religious order enamored of Scholasticism, the task of the theologian is contemplare, et contemplata aliis tradere. If one believes that scholasticism removed the practice of theology from the ascetical necessities of the average layman's life, or divorced theological reflection from the devout reading of Scripture, one is simply ignorant. There are hundreds, perhaps thousands, of contrary examples.
Finally, there is an overall difficulty in the implications of the Ressourcement position for the proper approach to the Tradition as a whole. If these new theologians are correct in claiming that the main threads of theological reflection as practiced over the past thousand years are largely fruitless and disposable, and that "authentic theology" needs to be recovered from some hidden trove where it has lain undiscovered in the writings of the Greek Fathers, then it becomes difficult to tell how one is supposed to perform this rediscovery. Doesn't one become a kind of highly-educated protestant? Isn't the entiref unction of the tradition between the Fathers and the Present that it has conveyed the former reliably to the latter together with all necessary clarifications and developments to render their testimony intelligible in the present time? And what are we to make of the innumerable commendations by great Popes and Saints for this supposedly dry and barren mode of theological reflection? Could it be that Ressourcement is just an excuse to abandon the Catholic tradition altogether, and reconstruct a new one according to one's tastes and creative inclinations?
The Ressourcement position is the worthier of criticism because it is the less obviously heretical of the two schools within the "New Theology" that have blossomed since the Council. The other is much more disturbing because it reveals a basic lack of commitment to any sort of apostolic tradition or faith. This is the so-called Aggiornamento school, emblematized by the journal Concilium. (Concilium recently devoted an entire issue to the need for the destruction of "orthodoxy" in Catholic theology.) These people are straightforward Modernists. They generally fit St. Pius X's description of Modernist theology to the letter: immanentists about the existence and nature of God; excessive use of the historical critical method to debunk and deconstruct scripture; rejection of the real continuity of the faith across cultures and time periods; subscription to any number and variety of dogmatic and moral heresies; extreme hostility to the authority of the magisterium.
One needn't wring one's hands about these guys, because it's clear that they are inventing a new religion which simply happens to share some key names and terminology with the one established by Christ. The chief difficulty with them, though, is that (again, as described by Pius X) they hide their many heresies behind vague, unconventional and metaphorical descriptions of their ideas. Rahner is an excellent example of this. In Foundations of Christian Faith, we read a "mystical" treatise on the essence and underlying realities upon which the Christian Faith is based. The language of this text is largely borrowed from Heidegger, and its style is full of circuitous neologisms. Because of the sprinkling of pious phrases and variations on standard doctrinal affirmations spread throughout the text, one might be tempted to think that Rahner's analysis is simply an updating of old Thomistic theology to fit the new philosophical methods of the German phenomenologists. Indeed, this is what Rahner is commonly described as doing! He even has his own "school" of Thomism.
But if you move beyond the stage of simply letting the verbiage wash over you and massage your consciousness, and try instead to get at the precise meaning of what he says, it is often extremely disturbing. He denies the reality of the life to come, except as immanent in the present life. He reduces God to the ground of our experience of mystery. He identifies grace, which is supposedly co-natural with human nature, with beatitude and claims that they are one single moment in our lives. He proposes the abolition of the traditional creeds and their replacement by certain more pluralistic and anthropocentric affirmations of commitment. The whole business is horrifying to anyone interested in preserving the truths of the Catholic Faith, because it very clearly does away with the Faith altogether. And to imagine that this man was held up as the chief theological hero of the Second Vatican Council!
So, to conclude, let me return to an earlier question: Why are these people so interested in escaping from the "dry" and "oppressive" network of scholastic theological analysis? If we read the responses to their work from before the outbreak of the conciliar crisis in the Church, we can find the answer very easily: their opposition to the medieval and post-Tridentine theological tradition is based on an opposition to the traditions of the orthodox catholic faith. And this opposition, this hostility, comes from a willful pride, which wants to free itself from the constraints of orthodoxy and the limitations of reason in order to express spontaneously an experience and a portrait of God (often shrouded in the "mystical") which is felt to be creative and personal, because it proceeds from the theologian instead of proceeding from the Word of God, and because it leads those who hear it to the feet of the theologian, instead of leading them back to Christ.