I don't like the moving Human home-thing just because of conservatism. I don't see/feel the new possibilities, just a change in the territory building approach. No strong feeling here, and I might be already in the process of changing my mind. Maybe if it roots in the Supreme Commander philosophy ("You are here. If you die, you die.") it could seduce me, but it would fight against the "nobody loose before everybody loose" philosophy in multiplayer. So maybe having one "bridge" ship (or just actual flagship) where all the players / incarnated commanders are and give orders from... Or say "if your personal bridge-ship is destroyed, you escape in a shuttle / are teleported into a friend's bridge ship. Maybe having the destroyed bridge/flagship spawn a shuttle that needs to be moved to a friend's flagship... but what would happen if that shuttle gets destroyed? Nah, startreck-teleported into a friend's flagship is fine. So you don't control "your" flagship anymore but you can still give orders. It just needs to be explained somewhere. I'm okay with new mechanisms as long as I can believe in them from a thematic standpoint. So yeah, maybe I'm already sold on that. Just be explicit with "how it works".
However I think I won't like moving AI home-things (at least not until the endgame). I think it would break the carefully conquest planning required for approaching the "center" of the AI's territory. But maybe it won't, I don't know. You'll need to sell me on that idea first. But for now, it would be a clear "nope" for moving AI home-things.
Ah, maybe something like an option or Minor Faction where, once destroyed, the AI Home Command Stations Cores use a sort of fail-safe that isolate the quantum computer thing inside into an escape shuttle, spawn an Avenger and is indestructible while the Avenger is alive, giving time for the quantum-computer-shuttle to escape and you'll have to hunt it down after the Avenger. Or if you have an insane firepower you could make short work of the Avenger and destroy the shuttle before it escapes.
I digressed, didn't I?