Barrie didn't like it--it was too much like a pantomime.
Do you have a reference for Barrie not liking the female lead - too much like a pantomime? Would be very interested to read it.
I would have said that it was, precisely, the British pantomime tradition that led to Peter being played by a woman - the tradition of the "principal boy" always being played by an adult woman. Like so many other things in the play which are so close to pantomime - the animal role, the rather effeminate villain, the audience participation...
Donna White and Anita Tarr are quite good on this in the intro to
Peter Pan In and Out of Time, and also Tim Morris in
You're Only Young Twice: Children's Literature and Film. And Morris develops the implications of the gender-bending in the various roles.