DUQ was never student-run. It was run by faculty/administrators, but students had a more prominent on-air role than in the current incarnation. At least by the early 1970s, though, the station was firmly established as a community station, albeit one licensed to a university.
Seems to me that most of the on-air people at WRCT are neither students nor alums of CMU. PTS still seems to have a hard time finding students to cover airshifts. That's usually the reason that student stations evolve into community stations owned by institutions of higher learning.
QED-FM is not successful financially, at least from a listener-funding standpoint. QED's annual report testifies to that.
YEP generates surpluses, despite having a very modest cume and a minuscule AQH, in part because it spends next to nothing to acquire programming. Were it to pay NPR anything close to what DUQ does, they'd need to increase their budget by about 50%. A local news operation would be out of the question. YEP's listeners pay for a music service, though. What makes anyone think they want four hours of news (or even two) in morning drive and an equivalent complement in afternoon drive?
DUQ said several times on the air last year what a tough time it was having financially. If it finishes in the red, DU must bail it out. I guess that isn't in keeping with the educational mission of the university, particularly since several have noted that students are not, at least in significant numbers, learning their craft at DUQ (certainly not in any way they couldn't via an internship at a commercial outlet).
If this were all simply about NPR content and Catholic theology or disgruntled diocesan benefactors, DU could keep the station and change the programming. When Xavier sold its station in Cincinnati, I believe the sale price was $15 million. Methinks that might be the driving factor.