I find that strange, I use Firefox as well, along with containers, ublock origin, and privacy badger (if those might make a difference) but my private browsing YouTube looks nothing like my non-private browsing youtube
My point still stands. If someone went to YouTube having never seen it before and they created an account, what they are introduced to is half mainstream drivel and half animal videos, reactions, viral videos, etc. Unless you are already interested in intellectual content, I doubt that most people are ever exposed to content that's... more meaningful. I'm not saying average Joe and Jane should be watching Lex Fridman, but it they at least knew that these kinds of conversations were taking place on social media then their perspective of the world might be different.