The TV stations will try to negotiate a larger monthly fee. If things don't go well they will make a PR campaign that you won't be able to watch the Dodgers on XYZ cable/satellite provider. It happens all the time.
Yep. Sports are why satellite and cable TV costs so much. Somebody mentioned earlier that people aren't going to subsidize sports anymore and disconnect but I doubt a large number will do so. Plus, there's no way local teams are coming through your computer/Apple TV/gaming system EVER without a satellite/cable/future model subscription. The league would have to agree to that and obviously that's not happening. Even if a settop box isn't the medium that LA residents watch the Dodgers on in 25 years, there is no doubt in my mind that you will still need to subscribe to a package that includes Fox Sports to watch a Dodgers game in 2037.