We have a Hisense Roku TV and it's extremely slow compared to the external Roku device, which is super snappy. What I do instead for the TV is just have it plugged into the downstairs computer. My partner uses the Roku TV as normal (mostly she uses YouTube) and for everything else I just have it set to the computer input or it's a different device on my AVR (Steam Deck, Switch, record player). Whenever I want music or media playing I just open Plex in browser or with the Plex program with either the mouse or the Steam Controller. On the upstairs TV we have the Roku Express and the Plex UI is nice with a couple extra options that aren't always available on other TV UI's.
I'm curious though, what about Plex do you think wouldn't replicate the streaming experience? Get it set up, get your hard drives pointed to the *arr services and set up a watchlist hook, something like Ombi or Overseer. I'm pretty sure you'd find it to be pretty much indistinguishable from HBO/Netflix/Amazon outside of the fact that each of those shows are now in one spot?
Once those 4-5 programs are set up, (Plex, Sonarr, Radarr, Jacket or Prowlarr, and Ombi or Overseer) your downloaded content is viewable on Plex, anything you watchlist on Plex is set to be downloaded.
If it's the "browsing through junk until you see something interesting" that you don't think will be replicated, there's various ways to do exactly that. Personally I went from looking at useless title cards and frivolous 1-2 sentence descriptions about the show to looking at the cast of shows and movies I already have, then adding whatever else they are in to the watchlist. But it's entirely possible to just point a "top viewed in last month" list via IMDB or trakt.tv and have those automatically downloaded. That should effectively solve the new/upcoming/popular media.
I find Plex to be far better than the streaming experience. I like to put together smart collections, like the Star Trek/Star Wars series, any new movies coming out would automatically be added to it - and their respective TV shows are shown in "related collections", like the Marvel movies and shows. Or if you want TV shows of a certain era, like an 80's specific playlist that you play in order or randomized. You can also set up other services like DizqueTV which allows you to create channels, so rather than putting your 80's playlist on random you just "change the channel" and some show is a few minutes in - the good old TV experience. It also has far better details about the media, from the actor list to showing panels for featurettes. It's like the better parts of Amazon Prime's information (although Plex doesn't have the trivia details).
Compared to self hosting other services, Plex is trivially easy to set up and to run on older hardware (sub $100 used). It is a little bit of overhead to get it set up, but from there it is only as much tinkering as you want it to be - I've personally had my server running for over 3 months now without restarting it just because I haven't felt like "maintaining it" (keeping it updated, tinkering by adding other services etc.). And when I used it with the Raspberry Pi it never went down until I took it offline.
Overall I think the most unreliable aspects of Plex are user error, subtitles, and then the online authentication.
User error is easy to avoid because Plex itself is so simple. For subtitles, as long as you provide your own you're probably golden. If you don't, Plex does have a very good way of adding subtitles easily however for niche content it can be hit or miss, also you need the "version" of the media it's subtitled for. So if you happened to get a movie with a movie production company cip that wasn't cut out suddenly your subtitles are a good 5 seconds off and * likely all of the ones you download will be like this because you have a different movie file*. Luckily this is also pretty easily avoided by using movie files you own cough getting a different edition cough. In reality this doesn't happen often, but it can be annoying when it presents itself and is just a byproduct of non-official sources.
And finally, Plex's online authentication. I've actually had Plex pass since 2013, I got it on one of those $79 deals in college and I can honestly say in all the years of reading about people's issues with online authentication I've personally never had it happen to me even during times where it's genuinely down for everyone.
I don't know if I changed the setting that's supposed to fix it and I don't remember, or if it's because I've always had my Plex server running over my local network or what. But whether my internet is up or down and Plex servers are working or not, I've pretty much always had Plex able to access and play my media locally (I rarely use remote streaming, which may be a factor). That's not to say I don't understand the frustration, I'm just very thankful for not having to deal with this particular one.
Also, much of the positives are true for Jellyfin as well, though I don't think there's smart collections to the same extent and it's a little more manual to get the networking aspect. Other than that though it's a serviceable program, I just don't use it actively.
If it's something else about Plex that you think won't scratch the streaming itch I'd be curious to hear about what it is.