Can a Catholic university be "great"?

Will Baude, over at Crescat Sententia, has a thoughtful post about Notre Dame's ongoing discussion about academic freedom, Catholic character, the Vagina Monologues, etc.  (Here are some earlier MOJ posts on the matter).  He writes:

[D]espite my being a libertarian and a staunch believer in the values of the Kalven report, I agree. There is no problem with a Catholic university deciding to construct a distincct institutional identity.

Now, caveats. I do think that being a great university requires a certain ideological neutrality on the important issues of the day. That means that a great university, ideas and views are to be expressed by individual scholars and students, not by the institution as a whole. That means, maybe, that universities that are avowedly and purposefully Catholic can't be "great".

But I am also a pluralist-- so the existence of libertarian universities, conservative ones, liberal ones, Catholic ones, seems to me a very good thing. For those who want an education that presupposes certain important moral premises, a university founded on those premises may be a perfect home. More power to them and those who work at them.

But I do think-- and I fully admit that this reflects the bias of my Chicago roots-- that there is an important function fulfilled by universities in society, and that the crucial core of that function, the enduring challenge to existing practices, codes, and policies, can be performed only by a university that takes no position on the issues of the day.

Now, I disagree, of course, with the claim that Catholic universities, to the extent they try to construct and maintain a distinctively Catholic character and mission, cannot be "great."  Or, more precisely, I am not drawn to any definition of "great" that excludes the possibility of "great" distinctively and authentically Catholic universities.  Also, I am skeptical -- even though, like Will, I greatly admire the University of Chicago -- that there really are any universities that "take[] no position on the issues of the day", or whose approach does not "presuppose[] certain important moral premises."