I'd love to switch to Jellyfin, but I'm still using Plex as their apps are ubiquitous...It comes pre-installed on most Smart TVs and is available on pretty much every platform.
There's also Roku, Samsung TV[1], LG webOS[2] and iOS/tvOS[3] apps in development if anyone wants to work on them.
[1] https://github.com/jellyfin/jellyfin-tizen
I also have Jellyfin installed and serving up the same collection of media for exactly this reason - sometimes it plays stuff that Plex won't. But the Plex app on my Samsung TV is far superior to the generic DLNA app I use for Jellyfin (I can't even remember the name of it; I tried multiple, and none were even close to as nice as the Plex one).
The library is centralized, though, so you need all the medial files on one place. Also, I'd recommend not running it on your router but on a separate device for various reasons (security, performance especially if you need to transcode). If you want to stream 4K without having to think about codecs you'll need decent CPU and GPU. For 1080p you should be OK with an integrated AMD or Intel, or even a decent SBC.