My ideal scenario is that the people you are talking about (people that care about rating change) would play matchmaker. It is just the rational thing to do as it is the area where, if you care about teamgames, is where you get the most recognition for your improvement/capability. This means that if you want to play a serious custom game on a specific map, you can host a lobby where you have a restriction based on that matchmaker rating which would be shown in the lobby.
What i would propose is that we keep global rating, but we hide it. Then we give tools for host to balance the game without having the global rating displayed.
https://github.com/FAForever/fa/pull/2887
https://github.com/FAForever/fa/pull/2903
maybe you can adapt the algorithm, so you can lock some teams (2 players want to play together, 3 others wants to play together).
And then you can check the % of balance.
What we end up with, is a global rating that isn't displayed at all, but that still exist in order to balance custom games, so that people that want to play 1 map can still do it. If people want to be competitive they can play TMM, if people want to play lot of different maps (without necessarily being competitive) they can play TMM.
Only drawback is for people that want to shine on 1 map, and get a high rating on it. They won't be able to display it. But i think this is fair, in order to achieve what we want to achieve.
Issue is that the pull request i've shown aren't complete and we need time / more dev to make it work out.
also since no rating is displayed for hosting a TMM or a custom game, there won't be any kick of 0 rating player anymore.