I think something like YC for films would be really cool, obviously it would have to be more than 20k but I bet some great work would come out of it. The hardest part would be finding a forward-looking person in that industry to start it.
This is a funny property of the US film scene though. Low budget in the US is a whole lot higher than for instance here in Germany. There are a lot of films produced here that make it into festivals that are produced on grants of under €20k. If it were done in connection with a rethinking of the way that films are distributed and was done all digital rather than using real film stock, I think you could produce some interesting results for relatively cheap.
They are headed by the crazy genius Lars Von Trier and an even more crazy guy called Peter Aalbæk. They do a lot of diversification, and have a lot of 50/50 ownerships. I'm sure that they would hear you out. They have a strong track record as well - they've won the golden palms in Cannes among other things.
