Go back a step. Why are sports so sought after? Well, they spend many millions of dollars on advertising, for one. That's more than the entire Seattle Symphony budget. How many people even know they play live movie soundtracks to popular movies here? Yet I don't even follow football and I can tell you about a team 2000 miles away which is in the playoffs. It's hard to avoid it. Why do they have that kind of money? Because they were successful in decades past.
I think a much simpler explanation is: a couple of professional sports leagues got big in the middle of the past century, for various reasons, and have used that success to gain a foothold into TV. Note that it isn't sports in general that are popular. There are really only 3 sports leagues that most of America cares about. Try to start a pro cricket league here and you'll just hear crickets.
The rich always get richer. In this case, the rich are getting richer using public money. It's not really about sports. Even the sports fans here aren't pushing to let kids play ball in the stadium when it's empty.