That is how client-server games already work. The server has the full world state, and each client has a subset necessary to render the world for that player. Ideally the absolute minimum subset, so as to reduce the potential for cheating (wallhacks, etc.).

The purpose of streaming is to remove the need for the simulation and rendering at all. The client is a dumb terminal that just renders frames and records input.

The moment you start making the client smart again — making it aware of a subset of the world state, making it do its own rendering based on the input — you've just reinvented current client-server gaming.