YouTube is one of the few websites which I wouldn't trust to have a video that I watched today be available tomorrow. The reason can be anything — local geographic censorship, copyright strike, uploader removing his own video, video becoming private, lots of other things I can't recall right now.
There are several reasons I do this, and most of it comes down to not trusting Youtube to keep content available consistently for the various reasons others have listed.
There is an added benefit. I have one channel I follow that does a LOT of q&a type videos from the audience. Because I download the subtitles as well, I can throw those into a database with the video titles and make a searchable database if I want to see what the host has said about a particular topic. I don't have to rely on my memory or go hunting. I can just query my database and know exactly which video/timestamp has the topic I'm looking for.
The other day I visited a 3 years old Reddit thread. OP posted a playlist for a certain topic. There were about 100 links to songs on Youtube. About a third no longer work. For many Youtube doesn't even tell me what the titles were, so I can't search for alternatives. I'll never know what those links pointed to.
If you have a system for delivering locally stored content already, then this lets you avoid all of the anti-user aspects of YT like ads and the recommendation engine.
