Already exists, it's what people refer to as "male olympics". As far as I know, females aren't banned from competing. It is just that they don't stand a chance in most disciplines. The whole point of female olympics is to keep males out.
Maybe they should accept that they simply aren't competitive if they can't compete against their own sex. There's no shame in it, most people aren't competitive, certainly so at this level.
Confidently incorrect. As an example - a banned Thomas salto had been developed and performed by a male gymnast first, and afterwards women starting trying to do it too. This is an anecdote example, but it shows that gymnastics is not some women dominated sport. As another example - four out of four named jumps in the figure skating are all named by male athletes who performed them first.
