The question is about society, not about individuals... why do we value this profession highly enough that we a) spend our time watching highly trained athletes play, and b) spend our money on products they endorse? (Those two things lead to the highly paid endorsement deals, presumably.) One possibility is that it feeds some primal instinct toward competition/aggression that we'd otherwise channel in more destructive ways. That's not an assertion or a fact; I haven't done any literature searches to see what the research says (although I'm sure some research has been done about this at some point). It's just a possibility.
I'm not denying that sports can provide a healthy distraction from things which are detrimental to society. But in absolute terms, the effect is quite minor in that if someone were to have the intention to inflict damage to society, the prevalence of professional sports wouldn't stop them. What concerned me about your post was how you said sports (possibly) "channel instincts that would otherwise be wasted in costly, bloody wars". Taking the rest of your post into account, to me it seemed that you were suggesting that the primary purpose of professional sports is to prevent violence on a global scale. I simply do not agree with this - it is a huge simplification to even imply that sports can prevent global conflict. Wars arise because of a big collective need (not merely desire) for resources, and not because people don't have sports to exert energy.
Of course there are other jobs for those who aren't academically gifted. But this is certainly one of them, and it's one that society values highly enough that it can lead to wealth, for those who are willing to dedicate themselves to the rigors of training.
On a fundamental I believe we are in agreement. However, I felt that you over-emphasised the role of sports when it comes to providing society as a whole with inspiration to find a job. The mere need for food, shelter and basic discretionary purchases would be more than enough to motivate the majority of people to get any job they can. Jobs are called 'work' and not 'fun' for a reason. If you're fortunate enough to do what you love for a living then fantastic. But not being able to live out your childhood dream would be a very weak excuse for not having the drive to get a 'normal' job.
As Declinerer mentions above, of course, this is only one way that you can make a load of cash without an academic background. Acting is an option as well.
My comments were centred on society as a whole rather than what a handful of people are eligible for.