LadyJuno - I was going to respond to the comments on my original post, but thought better of it at the time!
However, as you've mentioned womens football, this is what got me thinking about the minimal difference between men and women in lots of sports. I still think there is an argument for men and women to play football (and many other team sports) together, considering the size difference between male players in professional football I can't see a reason why there is still sex segregation other than pure patriarchy of course.
What also got me thinking was the changes that have been happening in long distance running (marathons), and the speed at which women are catching up on men in terms of times to complete the courses. I have heard this is due to better training for women (getting close to the amount men get), improved sponsorship and generally a better supported professional network.
I also wonder whether the physical and biological differences espoused on this thread aren't unduly tainted by the idea that women are the weaker sex, the society they've been raised in not appreciating their athleticism, their skill etc. and generally putting it down from an early age. Examples of this have been cited already in this thread, so it wouldn't be a surprise for me if this attitude was also a significant barrier to reducing the competition between sexes.
I suppose, linked to all this is the patriarchal assumptions about women being weaker etc. being supported by patriarchal scientists demonstrating "facts" about how important hormones, physical make up, muscle mass, leverage capacity etc. How much of our understanding of womens biology compared to mens has been tainted by these attitudes?
I fully appreciate that there are lots of sports where size, power etc... are the overwhelming deciding factor so please don't assume I'm arguing for a complete removal of sex segregation! But, it would be interesting to test the assumptions made and see if they really do stand up to a proper, objective analysis, rather than a subjective one.
There's a Phd in there if anyone smarter than me fancies it?! I'd love to read the executive summary and the conclusions!