They're testing that right now. It's going well.
I know, I mentioned that.
A server system that is separated from DMs/group chats, at least visually
Spaces.
On mobile on the element client, absolutely not. The spaces group chats show up in your DMs, and there is not a way to turn that off. Yes I know about other clients existing, there's one where you can turn that off, but it's not even mentioned on the main Matrix website.