Peter Pan was hardly considered a "man", though. More like a boy that didn't want to grow up.
Not until I saw a much more recent performance of the original Peter Pan play did I get the point of having a woman play the title character. I guess I never saw the Sandy Duncan version, nor a more recent version where the role was played by some famous woman gymnast. But on seeing a much more recent version than either of those, I don't remember who played the lead, I got it.
The point was to depict a boy who continues to grow larger, but remains a boy, rather than a man. At least with women of a certain build, it's not that difficult to get her to pass as an unusually large, but not physically mature, boy. Sandy Duncan has the right build for that. I see that the Wikipedia article shows a picture of her as Pinocchio—same principle.
Nothing at all to do with the sexually-charged
“drag queen” thing. Nothing at all about this sort of performance, even if directed at an audience of children, has any intent nor likely effect of confusing children about the difference between boys and girls, or about their own
gender sex. That's the point that the pedophiles, groomers, and their allies keep intentionally missing every time they bring up things like
Mrs. Doubtfire,
Tootsie,
Some Like It Hot, and so on, trying to equate those to inappropriate drag performances to which they want to expose, and in which they want to involve, children.