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.
That’s not true. Men’s gymnastics and women’s gymnastics are totally different sets of events and men would get trounced in a women’s event.
Can trans male who transitioned before puberty compete in male olympics while being pumped full of steroids legally?