Cocoa already runs on Microsoft operating systems. Or at least would given a few hours or weeks (at most) work

I disagree. The modern set of Mac OS X APIs is not OpenStep. I talked with Apple folks (ex-Nexties) about this not to long ago and they reaffirmed my belief. Anything is possible, but there's a big gap between possible and plausible.

In any case, it's still not clear why Apple would do such a thing.