As somebody who bought a Steam Link and tried to use it to stream games over a cat6 local network, the idea that Stadia would ever be successful was kind of laughable.
Spoiler alert: they didn't.
Google servers are much closer if not in the same datacenter as the game servers... network latency between them is negligible
So, (local input -> network delay -> reply / do graphics locally) == (local input -> network delay -> remote processing -> reply with h264 video). As such it's not going to affect things as much as local steam play which also works pretty well on local lan.