This seems like the perfect place to use InterPlanetary File System (IPFS) (
https://ipfs.io/). You can store and distribute files (including videos) using IPFS without worrying that someone could remove them. The only thing missing is a "UTube" front-end, and I'm not completely certain that there isn't already such a thing.
Maybe this type of project would be the thing that gets IPFS off the ground and exposing it to a more mainstream audience.