The purpose of sport for the companies that make money from it is, well, making money, and that's from advertising, gambling and entertainment, as you say.
But society grants sport a lot of tolerance and even encouragement that it does not grant to other such profit centers. What is the motive for society to do this? Answer: it dates from the time when sport was healthy exercise. Now that the ratchet of ruthless negative-sum competition has turned sport into something that does more harm than good, this social tolerance is highly inappropriate, and it should be revoked.
You are mixing pro sports with people playing casually. Pro sports is about players pushing themselves to the limit for the audience's entertainment. Modern day gladiators. You think of society like some noble, all-knowing and wise entity. It is not, I'm sorry to tell. Modern day gladiator games is all there is to it and the crowd loves it.
That's because reality mixes them. If it was just a case of professional sports ruining a few hundred lives for entertainment like in the decadent years of the Roman Empire, well that would be bad but on the basis of sheer numbers it would be small potatoes compared to things like a million deaths a year from road accidents or the major powers treating Syria and Ukraine like puppies fighting over chew toys, so I probably wouldn't bother to comment. But it's creeping into the general culture. For example: how many Americans have played football at least for a while in school? Now consider that everyone who plays American football suffers irreversible brain damage, and the total harm becomes substantial even on the scale of bad things happening in the world at large.
The purpose of sport for the companies that make money from it is, well, making money, and that's from advertising, gambling and entertainment, as you say.
But society grants sport a lot of tolerance and even encouragement that it does not grant to other such profit centers. What is the motive for society to do this? Answer: it dates from the time when sport was healthy exercise. Now that the ratchet of ruthless negative-sum competition has turned sport into something that does more harm than good, this social tolerance is highly inappropriate, and it should be revoked.