If you were just "some religious school" without any of the strictures of the LDS church then you wouldn't have the same connection to LDS recruits, because you'd just be another religious school. The church cares about sex and drinking and drug use, so BYU has to too. And I don't see anything wrong with that. The sillier aspects of the honor code bother me, as does the manner in which it's enforced and the inconsistencies in that enforcement, but not that it prohibits premarital sex, drinking, and drug use.

So if you were SMU or TCU you would be able to recruit whoever you want, but you also wouldn't get all the returned missionaries transferring to BYU, or any of the LDS talent like McKee.