Going back to the OP, I think that part of the reason this thread has turned a bit circular is the bolded aspect, and even that leaves out the criteria that others have brought up, namely: All-around athleticism vs unique skill sets.
For me, the very nature of a Mt Rushmore suggests a very heavy reliance on the 4th item in the OP -- Larger, transcendent impact on their sport and maybe even beyond.
When I think in those terms, and also keeping it American-centric, then I think the obvious nominees become:
- Ruth
- Jackie Robinson
- Ali
- Woods
- Jordan
- Gretzky (I know he's not American-born, but hockey is a very American sport)
- Pele (ditto on not-American born, but very instrumental in my mind with the explosion of youth soccer in the 70s)
- I might even consider Billie Jean King as I think her match against Bobby Riggs was pretty monumental to the cultural zeitgeist of the 70s.
Interesting as I look at that list, that there is only one white American male.