Also seems like a benefit for being able to use "any" screen to game on. The screen doesn't need to know how Stadia works or interface with the game controller, it just needs to receive video and display it.

Between USB polling rates, Bluetooth latency and OS processing, it's no wonder they wanted to avoid that entire stack and connected straight to Stadia. It's not a band-aid, those things together can easily result in 20ms of latency, which is an order of magnitude more than the latency of a fiber connection to Stadia servers.

What fundamental physics problem? Plenty of gamers, even competitive FPS players, found Stadia quite a good experience from a technical standpoint. Best in class, as far as streaming game services go.