Very interesting.
I'd pick
Ruth - There will always be arguments that he had areas of his game that were weak. But when it's all set aside his strengths changed baseball almost permanently. Mays may have had better overall skills, but without Ruth making power a major part of the game he might not have ever played. And Baseballs popularity in the years Ruth played changed the country in some subtle ways. Before and even after Ruth there was a stigma to professional sports especially in football and other sports that were big at colleges. It could be said that persists today in the rules of the NCAA. But there's no general thing against pro sports in the mind of the public.
Ali - Not for his stance against the war. But for showing possibly for the first time that an athlete could use his popularity to improve things for people in general. That was the reasoning behind picking all those out of the way places for his fights. And doing it in a way that actually made a bit of difference for the locals.
Pele - A huge star internationally, he spent what should have been the first few years or retirement playing for the Cosmos. His final game against his old club team sold out Giants stadium something that in the US in the 70's should have been impossible for soccer. I think it's fair to say that without Pele there would be very little soccer in the US. Considering how well our teams have done lately especially the womens team, he had a major impact on the sport overall
the last spot I'll leave open, with a few possibilities. I'm expecting them to be more than a bit controversial.
Many of the players already mentioned would be worthy choices but I like the less obvious ones.
Lance Armstrong - yes, disgraced and not generally all that good of a guy. But another whose popularity really made a difference for his sport in the US. I'd say probably not because of the cheating, but barely.
Bill France Sr. - founded Nascar. How different things would be without it.
Glen Curtis - Bicycle racer, motorcycle racer, aviation pioneer. Using ailerons instead of wing warping was a major advance just after the Wrights. Planes still use them today, so while his largest contribution was away from sports, He is a sports figure who made a major contribution the world in general.
(Many aviation pioneers and automotive pioneers were bicycle or motorcycle racers. Curtis is simply the most famous of the bunch. The Wrights raced as well, but briefly and weren't much good. They moved on to building bikes quickly)
Howard Cosell - Like him or not- and many didn't - he was a large part of making sports a major part of television. Where is the NFL without TV and Monday Night Football? Where are any of the fringe sports without wide world of sports?
Kraft and/or Bellichick - it's hard to separate the two. I'm becoming more convinced every year that the success isn't about Brady, isn't about who is there or not there. The team did go 11-5 with Matt Cassel as QB. So much of what they do is more about using a players abilities rather than trying to force them into a particular role or style of play. I can't recall any team using so many players who are either late round picks or undrafted. I do see other teams passing over good players in favor of guys they spent bonus money on who can't quite pull themselves together. Without a load of support from an owner a coach can't do that sort of thing. In many cities Bill would have been gone after his first season being 5-11. And to be sure he was a very mediocre coach with Cleveland.
But I also think it's too early for rushmore. If their methods become more the norm in the NFL and if that changes the game, then maybe. If it simply becomes a historic anomaly then no.
There's a rather large crowd of "others" who could be in. People who advanced the equipment in major sports, or altered the public perception of a sport. Many of them perhaps too obscure to be solid nominees.
Steve B