The Lack of Category

Something in a couple of not-so-recent threads – one about growing up a tomboy & the other about kids and gender identity – had me thinking about categories, since right now, boys compete against boys and girls against girls, though there are sports where that’s starting to change.
Two thoughts resulted:
1) I wonder what would happen if overnight we had people compete based on 1) build (height, muscle tone), 2) fitness level, and 3) experience in the sport/game. That is, if we got rid of gender altogether.
2) What if right now our real problem is that we don’t have enough categories? I mean, say we split the world up tomorrow by hair color instead of gender, Blondes and Brunettes. It’d force red-haired people to choose, and argue that there should be a third hair color. It’d force someone like me (who has kind of streaky hair) to choose. What if we told the Blondes they had to be delicate, graceful, and nurturing (how I have come to hate that word!) and told the Brunettes they had to be aggressive, powerful, and strong? Would L’Oreal make a fortune? Would there be Blondes trapped in Brunettes’ bodies?
I’m quite serious. Take all the attributes we normally assign to male/masculine or female/feminine people, and apply them to people with one hair color or another.
Sure seems arbitrary, doesn’t it? My guess? The whole men/women thing makes about as much sense.