I disagree, on all accounts.  I absolutely want score to be kept and I think competition is vital to self improvement.  

In the cases of men being stronger, this should be resolved by a system of meritocracy.  Only weak AF men would be fighting women.  Jui Jitsu people roll co-ed all the time. I've had my ass kicked by women.  

You again are lumping all women and men into two broad categories that I don't think are as clear as you are implying.  There are weak and small men out there and there are strong massive women who might be being held back from their ultimate potential by being allowed to only play against other females.

The ultimate minority is the individual.