and possibly not the first reason for the rule but you make my point for me---Being clean shaven shows maturity end of story.
I sport a beard every winter so I largely agree with your point but I think it's silly to make this a big deal of this... you know if you go to the Y you can't have a beard... you know if you go golfing at a nicer golf course you can't show up in flip flops... Hey I play better in flip flops but I know and accept I still can't wear them...
One of my co workers was recently let go, a reason she was let go was because she was "unable to follow simple rules..." the example was she was asked multiple times (2x) to change the photo on her bio to one with a solid background rather than a landscape. I REALLY hope and doubt that was the real reason she was let go but clearly that rubbed someone above her the wrong way. She was no slouch either.
The last thing I'll say is most young kids with beards look ridiculous, not all but most do.
Being able and open to follow stupid rules is important... whether it's not having a beard at byu, adhering to a dress code, or wearing my name tag on my lapel rather than my belt.