because the LDS nature of the institution plus the honor code drastically reduces the number of applicants versus the number that would apply to a similar school without those factors, which in turn drastically increases the acceptance rate.

Those same factors drastically increase the average credentials of those who apply-- i.e., highly qualified LDS students who wouldn't dream of attending a school like BYU if it weren't LDS affiliated and didn't have an honor code will apply and attend because it HAS those things.

IMO, the best way to measure a school's "prestige" is the credentials of the enrolled students-- this suggests what other schools the students COULD have chosen that chose BYU instead. And in the long term, having smarter kids enroll will increase the prestige of institution, because smarter people will graduate and go on to successful careers.