> These athletes train and risk their well being from an early age for the chance to 'go pro'.

My understanding is that there isn't much overlap between the sports with the most highly-paid athletes, and the sports with the highest risk to long-term health. Martial athletes, or even participants in full-contact sports like American Football or Rugby, aren't nearly as well-paid as participants in sports like basketball, baseball, or soccer. Heck, e-sports "athletes" are highly paid as well, and there is next to no long-term health risk in what they do.

I'm not sure why this is true, but I'll hypothesize anyway: corporations don't want to invest in athletes who can't retire to a life of being a charismatic PR mouthpiece for said corporation. If you get permanent brain damage, your value as a spokesperson goes way down. So corporations don't tend to be as interested in those sports—at least, from the POV of sponsoring the athletes.

There's probably an interesting curve you can compute by summing up the "athlete sponsorship expenses" for a given sport, and then dividing it by sum of the expenses of other market-interest-correlated activities that said corporations engage in, like franchise merchandizing or sports video-game production. I would bet that, the more risky a sport is, the less they spend on branding the athletes, in proportion to how much they spend on branding the teams, the country's league as a whole, or the sport itself.

And certainly, kids want to be athletes, regardless of the risk. I would argue that 1. many kids choose this path long before they can accurately weigh the risks and rewards of a career path, and then 2. they get stuck in it, because they (and their parents) have invested so much effort into cultivating their talent in the sport. (It's not simply loss aversion, but more like being 1% of the way into cornering the market on a lottery drawing by buying all the tickets. If you stopped there, you almost certainly wouldn't win, and would just lose all the money you put in; but if you continue, there's a clear point at which winning becomes increasingly probable, so as long as you can continue down that path, you feel incentivized to do so.)

This still means, though, that when you interview the average olympic athlete (the people who have "won" this competition) and ask them what they do for fun... they don't have much to say. They've put everything into this one bet; they have no other talents or hobbies or passions, because they never had time to cultivate them.

> Society does indeed value the role they as a profession play overall more than they do sports but not as individuals but as a service.

Yes, correct, that's closer to what I meant than what I said myself. :) Look at it like buying a smartphone: just because there's huge demand for the product, doesn't mean the average worker at a Foxconn factory is getting rich.

The middle-man—the hospital, in this case—is satisfying the societal demand, and therefore is "getting rich"; the doctors, meanwhile, only get rich to the degree that they manage to negotiate better pay from the hospital. That negotiation is sometimes explicit, but is frequently implicit, with a kind of collective bargaining going on just by social-status moves of doctors as a group causing the salary-level which no doctor with their "pride" would accept, to go up and down. (You can tell that this is happening because of the existence of "free clinics." Voluntary work is different-in-kind, so it frequently crops up in industries where the workers are too prideful to ever work "for cheap." Without this pride, you wouldn't see "free clinics", but rather budget clinics.)