This would keep movies alive after take-down requests, but you'd need to ensure the video wasn't poisoned (someone broadcasting they have a video when it's actually something entirely different). You would need to hash the video and store the hash on the blockchain. If Youtube changes the video (removes audio) you'd need to keep multiple versions of that video on the chain and clients would vote to confirm that those hashes were legit for when that version was up.
You'd also want to have some system to let you know if videos you have are no longer on YouTube (incase you want to delete them or if they have illegal content) and videos could still disappear, but only after everyone who has a copy decides to stop hosting them.
It would totally violate YouTube's TOS, but it would be the start to a more robust, distributed and democratic video hosting ecosystem.
It seems like one of the more appropriate types of data to be storing on blockchains.
Exchanging trackers for pow isn't a real advantage. Especially for large datasets (Youtube) where a third party will have to index the blockchain for reasonable to access it.
Currently, top piracy options like torrent websites and Kodi addons constantly get taken down by the government (through methods described in this article).
But what happens if a distributed YouTube exists with every movie in pristine 1080p quality, that lives on a blockchain so the government can't shut it down or issue DMCA takedown requests?