Technology

But even running an indexer on a YT-like scale would need serious money, even if you spread the hosting and streaming load around.

True but probably doable since it would be way smaller.

And for most users, this would not be attractive, as you probably would have to torrent the data first and view it later.

That's a good observation.

Then there is the issue with responsibility. If someone throws e.g. CSAM into the system, who could be held responsible?

The uploader. But I get that could be difficult.

Who would have to deal with DMCA notices?

Only the ones where the DMCA is valid. Which means US.

Who would deal with issues like “Dictator X demands all videos showing him in a bad light to be removed immediately!”

Do you realize that in many place such a request could be simply ignored until the dictator X does not get and order by a judge ?
Not to say that these are not real problems, but a distributed system is much more resilient to them, with the good and bad implications associated.

And: Opening a payment system is a serious can of worms, especially if you need it to work internationally.

That's a point that is more problematic since such system could|should not use something like paypal or similar services.