Most servers are not able to access the Google API.
Invidious report of the same(ish) problem: https://github.com/iv-org/invidious/issues/4045#issuecomment-1674373088
Any kind of federated alternative would have to use P2P in some way, and I’m not sure how well that would work. Peertube appears to be exactly that, but testing a video just now showed that it was all from servers and none from peers, so how well it would work with thousands or millions of people watching at once, I can’t say.
If I watch something, I’m happy for my outgoing bandwidth to be the cost for that. Most of us have plenty of that to spare, even if my patience for adverts is zero.
How would content creators be paid? Not my problem, but being paid by advertising has not lead to an improvement in content for the most part. Shovelling out videos with zero actual real content is not something I want to encourage.