The reason why a barbershop on a plane won't succeed is because wealthy men, the sort of passenger with the money to buy the necessary business / first class ticket, are quite often bald or thinning beyond redemption... I mean, if I went into a barbershop these days they'd certainly not think I was a customer, even if I did have the money for a first class ticket.
A salon for the ladies would be a better bet.
Still, I like the idea of an airline service that deposits one at one's destination in better condition than when one first boarded. Normally one gets off a plane in considerably worst condition.