when you are hosting something that is entirely dependent on a commercial entity to function
Eh, you can still get in with them down by hitting the local server, so I don't think this is entirely accurate.
Would I recommend it? No, I have a lifetime pass since the early days of it being offered and I just use JF. I recommend Jellyfin.
But I'm also not going to look down on folks who dont want to deal with auth or are unsure when it comes to opening a port on a firewall, access is something Plex makes easy and I get that.
So is it self-hosting? If they are running the server, no matter if its local, a vps, whatever, then I'd say yes. Whether or not it meets with my personal ideals are irrelevant.