Yes, and athletes know going into their careers there are going to be things they are going to have to do that are part of their careers whether they are fun or not. Sign autographs, shake hands, get accosted for photos at restaurants and the mall - even if you are a severe introvert or extremely private person. Play in a cold weather city, when you grew up in a balmy town with perfect weather where you've surfed all your life. Travel constantly, even if you hate airplanes, hotels, buses, and taxis. Live out of hotels in strange cities, even if you have a family. Share a locker room with a bunch of other humans when you are a germaphobe. Do tiring/repetitive interviews with PITA media personnel. Wear goofy retro uniforms/clown outfits (looking at you Chris Sale), and for some teams, yes, even how you handle your facial hair. I get the theoretical argument, but I'm not looking sideways at a team that wants their players to toe the appearance line to conform to a brand identity - even if it doesn't impact on the field performance. If a team wants to be like Mark Cuban's NBA team and make themselves the destination city for players by providing amenities, creature comforts and complete individual expression, and another team wants to be rigid about appearance for marketing reasons or even simply dumb reasons, that's fine by me. Let teams do their own thing as corporations as it pertains to employee appearance standards. If you are a fan of the team and you want them to change policies for any number of a million reasons... lobby away. I just don't see it for me and it certainly doesn't feel draconian in any way.
As to whether these facial hair policies helps the team or not, you'd have to ask psychologists whether conforming to the identity of the umbrella organization/ greater effort adds value or not. Hockey players conform to tradition to add facial hair - in spite of some finding beards intolerable because of itching. Teams wear goofy team shirts to create unity and bond ("Why not us?"). They have road trips where they voluntarily isolate themselves in search of a team identity ("Ubuntu") they can rally around. As mentioned above, the military shaves the head of incoming meat soldiers to set a tone, to psychologically unite them. I'm not saying all those things are useless... or that being clean shaven is a rallying cry, but I also wouldn't say the Yankees are wrong in their approach. Short of missing out on Samson as a free agent, who knows what real impact it has had. And as Adam Dunn said, it grows back... usually.