Dude. The Stadia consists of a wireless-only Chromecast and wireless-only gamepad. Explain how you “plug in” a device which is wireless only, would you? You seem to think it’s some sort of box like an Apple TV box, but it isn’t. It just a little Chromecast stick which goes into your TV and gets wireless internet and a gamepad which doesn’t plug into anything and connects wirelessly itself.
The router will be connected wirelessly to the Chromecast. That is the point of failure.
Later the Stadia as a service will expand to other devices, some of which can be wired.
The fact that we’re having this discussion long after preorders have started shows that there will be a lot of surprised and disappointed people out there.