There’s likely a sizable population that cares more about convenience, cost, and predictability of outcome.
Premium barbershops currently compete on experiences vs outcomes: giving you a glass of whiskey, providing great ambiance, etc. If robots become the default for basic haircuts it will make premium barbershops seems all the more luxurious because you have an actual person (an artist!) cutting your hair. Perhaps they'll be able to raise their prices even more.
1st Disclosure: I'm one of the co-founders of On Deck and the OP is in the On Deck Fellowship.
2nd Disclosure: I thought this idea was completely crazy when Manish first brought in that absurd mannequin with the replaceable beards. Now, the more I think about what he's building and the opportunity space the more I love it.