>Should they just hand that over to Netflix or something?

Not necessarily netflix but you should be able to watch all games of a given team and league on a single site/service. Something like a league wide streaming site isn't impossible. You shouldn't have to subscribe to 5 different providers to watch all of you teams games.

> The rights to the sports are owned by different entities, sometimes locally. Should

Sure but that doesn't mean the game can't be shown locally AND on a streaming site that carries all the leagues games.