There is some debate today about universities and some say they do not teach much. You can see this in Michael Huemer. But the problem was already seen by Allan Bloom in The Closing of the American Mind and he saw the issue in a wider context--an issue about the Enlightenment itself.
For there were people from the very beginning of the Enlightenment that were against the whole movement. [Jonathan Swift in Gulliver's Travels where he saw the rule of the intellectuals as them siting on some floating Island and ruling over us plebeians.]

I myself do not see much of an answer. However I can see that even in the Middle Ages before any of that started there already was this issue about Faith and Reason. But the Middle Ages had more or less come to the conclusion that you need both and some kind of synthesis between them.
I would point out that Hegel came closest to defending faith and reason in the most rigorous possible system--if not for the fact that he has been used ever since then for the exact opposite.
Faith with reason in the middle ages was the idea that both are compatible, but no one made the whole into a organic whole.

Leonard Nelson also has a clear defense of faith [That is the Kant Friesian School] but I can not tell if the difference between him and Hegel is all that significant. [The dinge an sich with Nelson is detected by a third faculty of the mind immediate non intuitive knowledge.  It does not seem all that different than Hegel'e getting to God through the dialectic.]
[I think that in terms of STEM universities are doing great. Allan Bloom was talking about the other insane departments.]