I tried Plex years ago, and it wasn't to my liking because it was philosophically like Windows (Load the filename up with show information and constantly ping the internet for matches) instead of macOS (Metadata where it belongs — with the file).
I'm considering adding a Sony phone to my household, so now that Plex is in the news, this reminded me to check it out again.
If you're purchasing everything through iTunes (do people still purchase stuff through whatever is "iTunes" now? I guess I don't know that either) I assume its handling transcoding/different device playback and delivering all the metadata for you.
Also once Plex pulls metadata down you're right that it doesn't store it with the file but AFAIK its not constantly hitting the net to pull that info down - it keeps a local cache.
I will say at this point - I wouldn't bother switching to Plex and look for an alternative like Infuse. The company is clearly under pressure to monetize beyond the Plexpass subscription you can buy. They've been steadily adding crap no one wants and automatically jamming it into the home screen of the app where you then have to go turn it off. Its just a matter of time before they cross a line somewhere and people jump ship. When that happens I imagine some of the open source alternatives (Jellyfin) will see a huge influx of development. I haven't switched just because I don't want to be hassled with figuring out a new system.
Ironically I like Plex & Infuse for the reason you hate them, I just give them files whose metadata is just their filename and they can match them to what they really are. No need to keep all the data in media container tags, and a thumbnail/poster that will be pixelated in a few years because something will scale it wrong.
Sony is a valid option given their love for DLNA but I just never really liked the tech. Hell, I have statically-reserved IPs & DNS-registered names for everything in my home.
EDIT: Oh, I forgot -- the main reason I moved off Plex (and would hate iTunes Home Sharing) is I don't leave my PC on. I switch it off daily and don't like to treat it like a server, and to keep using Plex would require setting up a NAS or something (I had my collection on a local SSD for a while).
To some extent, it's self-reinforcing. Once the FireTV gets a lead, all it has to do to maintain/extend that lead is reasonably support playback of whatever new format/source and Plex works great on it. If FireTV supported TV as well as TiVo does, it might end up with 100% of the living room display share.
(I also have Plex sharing to devices outside the house, but that's a <1% use case, mostly when it's us traveling somewhere and the kids wanting to watch something that's on Plex.)