There is no doubt that Thorpe was a terrific athlete, competing against a severely limited talent pool. Only 28 nations competed at the 1912 Olympics, and looking at pictures of the U.S. athletics teams from that era, it’s obvious that the domestic search for talent was hardly exhaustive. Big fish, small pond.
The argument for Thorpe, though, isn’t just that he was an Olympian but he was able to compete at the highest level in MANY sports.
Multi sport excellence is a characteristic of the very greatest athletes. Indeed, it is something professional sporting league scouts look for; a young man who is very good at only one sport is less appealing, far less likely to work out, than a young man who plays many sports very well. Wayne Gretzky was an exceptional baseball player and played tennis and golf very well; while not a beast like Bo Jackson, he was a marvel of stamina, endurance, agility, and hand-eye coordination, which is of course why he proved to be pretty good at anything he tried.
It’s true Thorpe was not playing against the biggest talent pool, but he did compete against what he could and was amazingly versatile. He might well have been the best ever.
Personally, I would go with guys who were head-and-shoulders better than anyone in their chosen endeavor. It’s impossible to say exactly how all-around athletic people are, only how well they have developed for various competitions, and there’s only the decathlon and similar events that have reasonable scoring systems for mixing different disciplines - but even there, one can argue with how exactly each event is weighted. So I would go with those most in front of others in their chosen discipline.
And the definitive answer to that is Donald Bradman.
So far ahead of anyone else it’s just ludicrous, especially given how closely clustered they are after that. Per wikipedia: “In order to post a similarly dominant career statistic as Bradman, a baseball batter would need a career batting average of .392, while a basketball player would need to score an average of 43.0 points per game.” I think the article cited also said 25 major victories in golf, though individual sports titles are somewhat of a different animal than averages in team sports.
But then we start getting into really weird questions about athletic specialists, right? Edwin Moses winning 122 consecutive races between '77 and '87, setting a new world record again and again and again; Michael Phelps winning Olympic gold in his event of choice in '04 and '08 and '12 and '16, setting eight world records in it; and so on.