As someone who develops and distributes a small application exclusively on Flathub, I prefer that everyone uses the exact same package on every system. That way I know that if something doesn't work, the issue should be easy to reproduce.
Recently, there was a situation where a user indicated in the comments of a release announcement that a newly introduced feature “doesn't work”. It turned out that they installed a third-party package from the AUR (that wasn't updated yet) without knowing that this isn't the official and up to date version.
As others mentioned, running a minecraft server by itself is pretty easy. If you want additional features like a Web UI, multiple servers at the same time etc. you might take a look at Crafty Controller.