I'm pretty far from the multiplayer game dev scene, but isn't this close to how a lot of multi player sync works anyway? Just* distribute everyone's control inputs and have them all run a deterministic simulation. And then I guess you would run the same input cheat detection on all the honest clients, which are hopefully the majority... Is this impossible or did I just reinvent something that already exists?
* Yes, I know. But at least I know determinism is possible.