Why do they pay for the right to broadcast, though? Because they want people to watch, right? Isn't receiving their signal and transmitting it to more people who can watch it more easily and with higher quality doing them a service?

If you look back before cable TV, broadcasters transmitted their signal and the only people who could watch it were those with suitable equipment within range. Broadcasters competed to get as many people as possible to watch. Each new eyeball (preferably in pairs) meant additional revenue for them with no additional cost.

Then comes cable TV. In addition to access to new channels, it also provides the benefit of being able to watch regular broadcast channels even when you couldn't receive them over the air. That means more viewers for the broadcast stations, and thus more revenue. Why, then, should broadcast stations get paid for distributing their signal to more people, which is what they want anyway?

It's clear to me that this is what the law says, and since the Supreme Court's job is to interpret the law, it also seems clear enough to me that they made the right decision here. But it doesn't seem like a very good law.