Independent of government funding
You mean "commercial"?
We already have Nick Jr. and Disney.
We also have the Discovery Channel. Have you taken a look at some of their offerings lately? The high-end science and nature programming doesn't pay the rent. "Super Sharks from Outer Space" does.
Or do you mean pay per view? PPV would turn public TV into a cable network, so it could control access, and would price low-income people out of the service.
I don't know what it would do to public radio.