Nope... By 1981, they had stopped taking all federal funding.
https://en.wikipedia.org/wiki/Sesame_Workshop#Funding_sources
And lots of other PBS programs are nowhere near as lucrative as Sesame Street, which is why they go after funding. Shows like Frontline or NOVA don't have a lot of merchandising opportunities....
Dude? You're not telling me anything I don't know, or that arts and public broadcasting don't already know. You are literally suggesting that we replace federal funding with... funding sources that already exist.
Individual artists, arts organizations, public broadcasting stations all already go after state grants, private grants, corporate sponsorship, membership drives, fundraising drives and more.
Of course, relying heavily on private sources has its own pitfalls. Funders can often be capricious; some chase fashions, or push the organizations to do something trendy, or pursue off-message programs because some incredibly wealthy person heard that Tuvan throat singing is the New Hotness. Bigger funders are targets for many philanthropic entities, whose needs are increasing as public funding is increasingly cut. A handful of the "whales" invest in their own projects; e.g. "vanity museums" like the Broad Museum in LA, or Rubin Museum in NYC, which in turn compete for... wait for it... grants and private funding.
For example: If we eliminate the NEA and NEH, that permanently cancels $300 million in funding for the arts. That $300 million does not magically appear somewhere else.
It also has almost no effect whatsoever on the federal budget. Those two programs are literally 0.006% of the federal budget. These cuts are not about fiscal responsibility, they are ideological.
Public broadcasting also receives private funds -- and it's not enough. Again, states are cutting their own funding, not increasing it; and cutting the miniscule amount of federal spending does not magically free up state funds. If federal funds are eliminated, then that either puts more funding demands on private donors or, more likely, is going to lead to stations cutting back or closing up shop.
Or....
You don't seem to know much about arts funding or public broadcasting. Which is fine, but if you're going to make suggestions, it
might help to listen to someone who knows a bit about it, or at least do some research on your own to see how it works. Just a thought.