So many things that invite the spirit for kids as they study and learn at BYU make it special.
Not allowing beards doesn't strike me as one of those things. It strikes me as a relic of an earlier time where beards were used as a way to separate oneself from the mainsteam. That's just not the case anymore. My dad was a grad student at Ohio State in the late 60s and early 70s, and he confirmed that beards then definitely carried a message. But even by the 80s/90s, he didn't see the same message attached. It's 2024 now, time to move on.
I also agree that lots of young men have patchy, scraggly beards and whispy, pedostaches. But that's just something to laugh at and help educate them at an early age on the difference between good facial hair and bad facial hair. No reason to prohibit it.
I also don't think they overall cleancut reputation of BYU would be affected by having dudes with beards.