Plenty of people have tried to do this. You're right in saying you aren't the first to have the idea. Its in the "too hard" basket for good reason at this point, clubs have limited funds and, as you say, they spend them in other areas. The ROI on streaming for most local clubs is not going to be good, the money is far better spent elsewhere.
Okay, well don't stream. But upload the game footage (which will be filmed) onto social media for people to watch post game. That isn't too difficult, is it?