Going back to 'could a mediocre male footballer compete with premier league women', I'd have thought not, as they'd still have greater physical capacity to be good at that sport, so an unfair advantage.
They just wouldn't have trained as much, or be as talented (if talent is some combination of mental and physical attributes).
That takes me down a path of wondering what attributes are measured and whether some come about as a result of training. Then, could you end with something like a Paralympic points system, based on physiological (and mental?) capacity.
Is it possible that for some sports, requiring a suitable blend of attributes, a governing body might decide that 'no unfair advantage' could be assessed that way?
That would be totally at odds with a system of grading, selection and winning based on performance. It also tramples on the idea of Olympians as exceptional - as sometimes going beyond what anyone thought was possible (look at women's marathon, so very recently). Athletes proving what they can become, re-writing the physiology books, not what they were judged as having capacity to become based on old knowledge.
Could exceptional women then be banned from women's sport for being too good, rather, too exceptionally capable? Probably not, much more that physically mediocre men would be allowed in. But my point is that any judgement of advantage based on capacity, changes the ethos of sport from 'any of you lot, go on, surprise us' to a rather deterministic equation of capacity plus effort (yup, I realise that's exactly what sports scientists, trainers etc already work with). Conceptually though, it's different.
Also, this will have a far, far greater impact at the lower levels of some sports than at Olympic levels - if and when governing bodies have to publish their 'advantage assessment criteria' rather than judge each individual case on its merits.
It very much sounds as though that's already happening - and without any proper assessment of advantage - if that marathon runner is already competing against women.
Club and county running championships for example would be changed massively, if any man with slightly below normal testosterone and a stated inclinitation towards femininity (this season anyway) was allowed to compete against women.
The 'unfair advantage' assessment is, as purple said, the failsafe of this policy. I'd like to know more about how it might be assessed - and at what levels of competition it's required.