Yes, a small subset of games have downloadable server software; the ones that do are able to do so because it’s self-contained and unencumbered by proprietary components that can’t be redistributed.
Most games don’t, and they won’t be able to.
Licensing restrictions aside, how are you supposed to package a modern microservice-based network of servers into a single package that can be run on consumer hardware? And abstract over the specifics of the cloud environment you targeted so it can be run elsewhere? It’s pretty much a nonstarter.
Running a single dedicated server on a home computer to play with whatever community you've curated requires none of these. Any sane game server architecture would already be essentially a single executable since you want performance and synchronicity within a single "match" or "world".
You say most games won't be able to release server software. Can you provide an example of a game which could not possibly be disentangled from its cloud architecture? I'm having trouble thinking of any