I think we already know how this story plays out. It would still be a great school and provide a great LDS-focused experience. However, over time it would drift along with popular opinion and culture to the point that it more closely resembled a composite mixture of the surrounding secular community.

This wouldn't necessarily a bad thing, but I think that there is still some value in a school that is directly tethered to the church. I think BYU (in it's current format) is a great way for the church to show how "higher education" and "religion" really can co-exist.