> os.rename(overwrite=False) by default will do less harm than the opposite,

Disagreed.

> Then I believe that having a small chance of overwriting file just created
> at exactly the same moment on a POSIX is a small price to pay for function
> that does safety check before rename on a platform that doesn't have such
> functionality at all.

Disagreed.
If you need the functionality, it's *one* additional line of code. Not
every trivial function deserves to be in the stdlib.