It's not as though this is a new question. The question has been discussed (from a Roman Catholic perspective) in Newman's "Idea of a University", extended and fleshed out more by James Sire in "Discipleship of the Mind", Richard T. Hughes in "How Christian Faith can Sustain the Life of the mind" and "Models for Christian Higher Education", etc., and in the work I would like to quote from here, an essay by Russel Kirk entitled "The Revitalized College: A Model", which is found in the book "Education in a Free Society," edited by Anne Husted Burleigh.
What, then, is the chief end of a college of arts and sciences? Why, to enable a body of senior scholars (the professors) and a body of junior scholars (the undergraduates) to seek after Wisdom - and through Wisdom, for Truth.
The end is not success, pleasure, or sociability, but wisdom. This wisdom is not the same as facts, utility, training or even knowledge. No college can confer wisdom, but a good college can help its members to acquire the means to pursue wisdom. Wisdom means apprehension of the human condition, recognition of reality, and the experience and possession of high knowledge - together with the power to apply experience and knowledge critically and practically. Although it is still relatively easy to find learned fools, true wisdom is rare; and so must wisdom always be. Still, in the hope that wisdom may not be extinguished altogether in our generation [TKP - Kirk wrote this in the 1950's], I endeavor to present to you model college that might help to make the acquisition of wisdom less difficult than it is at present; a college some of whose graduates might be philosophers (lovers of wisdom), and many of whose graduates might be, at least, men of right reason, humane inclinations and sound taste. (pp 133-4, Education in a Free Society, ed. A. H. Burleigh, Liberty Fund, 1973)
With apologies to the great American philosopher-poet, Pete Seeger, "Where have all the philosophers gone?" It seems to me this particular end of an institution of higher learning has gone by the wayside long, long ago - perhaps when it ceased to be the consensus that "the beginning of Wisdom is the fear of the Lord".... our colleges and universities, today, for the most part seem to be completely divorced from the seeking of wisdom and intellectual soundness, and married to a new conception... the ability to get a nice job where one can be personally (individually) fulfilled while making lots of money.
I'll admit to being a cynic about our institutions of higher education (including my own), but I honestly want to think out loud a little about where colleges went awry (and invite your thoughts by way of comment). Kirk in his essay is probably a little more optimistic in his assessment of the ability of institutions that aren't fully Christian through and through to help students truly pursue wisdom - but his insights do point to cracks in the foundation of American higher education that were already gaping chasms in 1971 when he wrote the quoted essay.