An observation I made is that the tournament career system is supported by the entire cadre of players and families, of the kids who won't win one of the prize jobs. One reason is we just don't know which 18 year olds will rise to the level needed to win a symphonic audition a decade later. I've always been ambivalent about this, but don't have a good idea for how to reform it.
I majored in math and physics. My parents didn't cringe, at least quite so much. I became, quite honestly, a mediocre physicist at a time when you had to be a research superstar to apply for a tenure track job at a third rate college. The consolation for me was that a mediocre physicist could still earn a decent living doing something in industry, and I'm now at a late stage of a satisfying career.
I also work on the side as a jazz bassist.
Corporate sponsorship pays the bigger amounts: that is a side job with its own commitments. Prize money: by definition not available to most.
Directed pay is a tiny fraction of it (stipend level), even at the highest levels.
Athletes have other jobs.
Again: a bad model for mathematicians. None of them are going to be signing merch deals. Most aren’t winning prizes. I am afraid that mathematicians are just going to have to keep doing all the other jobs they already do.
At least some countries have programs where (candidate) Olympians get professional support and a stipend.
See for example https://www.uksport.gov.uk/our-work/investing-in-sport/how-u..., https://www.dosb.de/en/themen/athletes/services-for-athletes