The real problem isn't even live sports, it's live sports blackouts. If my NHL Gamecenter account (or similar service from other leagues) allowed me to watch local games, I wouldn't need cable.

I'm sure the leagues are incentivized to maintain local blackouts as a way to capture enormous deals with various sports networks, and also to drive gate revenue, but cutting out the league middleman does afford them the ability to do some nifty things, like directly charge consumers of their content.