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That would mean the networks lose a lot of money, and they're not exactly profit machines as it is

You're looking at this precisely how the NFL and MLB want you to look at it. The reality is that MLB and the NFL are congressionally-sanctioned monopolies that make a ton of money for the owners and players. Ever see an episode of MTV's Cribs?

The networks are "not exactly profit machines" as you say because the leagues are charging them so much. The networks in turn have to charge an arm and a leg to sports fans to make up for it. Sports fans are rebelling with both illegal and legal options like Aereo.

I don't know how things will play out but when you have a situation where a single person is making over $150,000 to play a single game of baseball, that's probably not a sustainable business model (see http://en.wikipedia.org/wiki/List_of_largest_sports_contract...).