Should we stop splitting sports by gender and just let everybody compete together?

No more men's and women's league, no more "gender eligibility" requirements, a common dresscode, same standards and rules for all.

Edit: since it looks like people missing the word let: the suggestion isn't to force desegregation. It's to allow it or even make it the default. Someone else made a good suggestion: segregate by attributes specific to the sport. In boxing it's weight class, in basketball it could be height, in biking it could even be doped and non doped. Sex and gender need not be the very first thing to segregate by.