MPV is great, I use it all the time. It’s fully replaced VLC on my desktop.
It is not an “alternative to Jellyfin”. It does not offer many “comfort features” like (synced ootb) watch tracking. It does not transcode at all, and it doesn’t even run on devices that need transcoding most, like smart TVs.
These two applications fall into two different categories, and they will never replace each other. One is a media player, you throw mpv any video file, it puts it up on screen, great. The other is a media server, it allows you to sign in, browse your nicely organized library, and click play on the movie of your choice, very cool.
Even the idea of opening SMB or NFS to the entire internet just so your most technical of friends can manually download and watch a movie is insane compared to setting up Jellyfin. Reminder, not everyone has the connection to stream a full 4k bluray rip, transcoding allows those users to watch at all.
Besides,
Web push for notifications. Sure, there’s privacy implications, but it’s already near universal. There’s other options like ntfy.sh if you’re not limited to existing infrastructure. UnifiedPush also works well as a protocol for push notifications.
Everything else can be handled in-app. Password reset will have to be done by an admin, though it’s completely doable for a small selfhosted service.
Some of the downsides OP listed may or may not always apply, but there are always downsides. Either you have to set up your own email server (with extra maintenance burden), or your “selfhosted” app suddenly relies on third party infrastructure, like your email provider (or those of other users on your instance).