Earlier quoted context omitted.
By directly connecting the controller to the service via WiFi it removes any potential issues with the device having to act as a proxy for the controller input. For their dedicated Stadia set top box it isn't a big deal (as they will control the hardware) but when used with phones, third party STBs and such it can be problematic. Google will have no control over the WiFi hardware in all these devices and many cheaper…
Yes, I was thinking along the same lines. It seems like the combined latency of bluetooth, passing that input through the OS, browser, then out to wifi could be considerable, especially if the machine's wifi and bluetooth chips are not optimized for low latency. Since Google makes the hardware of the controller, they can use all the lowest latency chips and drivers possible. I'd be very interested to see some latency…
How about a controller with an RJ-45 so I can plug directly into my router :)