I get that sometimes it's great to archive a video in the case it get's deleted from YouTube, but in my case this very rarely happens. I watch the video and I'm done with it. If I can't re-watch it, this doesn't really matter to me.
1. Removal of ads is a pretty big reason for many.
2. As you already note: you can't stream a video again if it or the entire channel has since been taken down due to copyright claim (spurious or otherwise) or other complaint. This may matter a lot more to some people than it does to you, depending on the content they are consuming.
3. Some may be downloading for offline play. You can do this with the official YouTube app too, but not without paying for Premium (which seems exorbitant to me) and still being subject to the takedown problem.
4. Local indexing: if keeping reference to videos for future rewatch or sharing, arranging then in your own structure may be more convenient than maintaining bookmarks to YouTube copies or searching for them each time.
5. Some mix of the above, and likely other reasons I've not considered/remembered.
For me, the same reason people used VCRs, and I don't mean "copyright infringement" --- saving stuff to watch later or when I don't have an Internet connection, or only a slow one. The majority of what I download only gets watched once and deleted.
Not that I would let them anyhow but YouTube starts recommending really trashy stuff when it finds out you're a kid. The tamest of it being stuff like adults playing with toys in a very childish manner.
Not to mention that sometimes streaming from youtube might not be possible (internet down) or cost prohibitive (mobile plan abroad), or just plain removing those shitty ads.
at least a dozen times in the past couple of months i’ve searched for videos i’ve previously seen, using almost exact title language the search just wouldn’t give them to me. the vids i did find was only because i ultimately remembered the names of the channels they were on and had to trawl through them directly to find it.
it’s to the point now where it’ll just be easier to grab videos i find interesting and be able to find them later with much less hassle.
for me it wouldn’t be an issue if they hadn’t broken their search so badly.