A Systemd unit as shown in [1] does it too without using containers and with fewer moving parts of using containers. I use containers every day at $work. I have been using containers since before Docker was a thing. In this case, it's entirely overkill: Systemd units use the important things like cgroups already.
For the upgrade: depends. You do need a container image regardless, and I have not seen official ones. Upgrading servers in Minecraft requires upgrading clients to match, and my kids prefer to play, more than upgrade. (Unless a biome is released. Then it must be immediately available to them.) But then again, I just need to download the binary with a cURL call. And if the configurations change, Docker won't help me there one bit anyhow.
[1] https://github.com/dash0hq/minecraft-server/blob/main/drople...