If we didn't have an honor code, BYU would quickly become the U of U. Or "any other school." I see and hear some version of that on the board or in LDS circles, and while I understand the premise, it strains belief.
This viewpoint requires a rather stunning lack of confidence in LDS young people and their upbringing for one thing. Force them to live a certain way with a son-of-the-morning-like pact, or BYU will becomes indistinguishable from other places. This is going to happen to an environment made up nearly entirely of high-achieving LDS youth, taught by LDS professors. So much for church precepts having enough actual value that bright young people, surrounded others like them, might actually choose to continue abiding on their own. The whole mission experience--whether it be preparing for one or actually emerging from one with core convictions--doesn't appear to carry much weight. Temple marriage or covenants? Also an insufficient motive.
If it's appearances alone that concern you (and that seems a bit of a misplaced priority), I'd ask if every LDS U of U, UVU, or Utah State student looks dresses or look like Ke$ha or Machine Gun Kelly. In my experience, that's a hard no. Remove the archaic, baseless and utterly silly "mustache-good-beard-bad" rule, and you'll see more beards and 5 o'clock shadows. The horror. Will the ultimate effect be BYU's student body becoming indistinguishable from that of a state school, or will you see a minority push boundaries in terms of dress & grooming for attention, as they figure themselves out, etc. as most go on resembling what you'd see in a typical LDS ward?