You hit the nail on the head. The distribution of local server farms in Google's network is much, much larger than people assume (has been for awhile).

There's also a chicken-egg effect that Google's still interested in for secondary reasons. Reverse the question: assume Stadia takes off and becomes the "killer app" of gaming (big assumption, but still). Will local municipalities continue to tolerate crap networks if it means they're left out in the cold on this thing? Google's still interested in improved network infrastructure and has the clout to play incentive games to make that scenario more likely.