This suggestion, however makes it a bit different.
As you might already know there was that barbershop stuff on retail (was it post cata?) and we all witnessed they absurdity and consequences of it. I dread to recall it.
Let's make it with a different approach this time. Instead of buying a haircut at the barbershop ingame we could make it as a ... Let's call it a form of supporting the server.

Actually it could be quite handy for both, the server and the players to have a service where you could change the appearance of your toon for some either coin or irl money.
I understand that buying a full out appearance when you might only wish to change the facial hair, but then there could be a dialog option at the innkeepers for such services at the cost of the gold. However to change your skintone or facial expression should take a more seriuos approach and cost $$.
Yes, monetization, i know, but it's not like you buying some powergems or potions (please do so not, ever) What's interesting is that it makes no serious impact neither the gameplay nor the economy. Also there's nothing game-breaking.