Controller -> Stadia device -> router -> Stadia
is a helluva lot slower than
Controller -> router -> Stadia
And also drastically simplified the "Stadia runs on all kinds of devices" requirements.
It seems like a smart architectural decision.
The data trip through unoptimized stacks on the hardware would really hurt.
And optimizing a diversity of different hardware devices (some of which predate Stadia) sounds like a support nightmare.