Call your government reps.
I'm not sure why you would assume to the contrary.
They do the same things with public schools (pulling educated teachers to teach in private institutions) and with medical care (pulling physicians into private concierge practice).
If all the rich people had to take public transit and send their kids to public schools, they'd start investing money and (human) energy / capital in making the public infra better.
The investment of resources by rich people into their own private enclaves is entirely rational and can be solved only by wealth taxes that preclude such action (by making it impossible).
It certainly isn't stopping anyone from improving public transit, but it seems like you believe it's this and not any one of a bajillion actual factors to blame.
Google's use of resources does not occur in a vacuum. Moreover, if cities decided to pass laws that would slowly transition all road infra away from private vehicles to shared public transit, then Google would lobby against that.
For public transit to function well (i.e. competitively with private vehicles), traffic needs to be much reduced (e.g., imagine no traffic lights and no traffic). Google's private cars on the roads do not move us in that direction. There is no doubt that they are technologically impressive, but they do not provide greater utility than investing in shared infrastructure would.
While it sucks for many other reasons, autonomous vehicles are actually a very good solution to public transit in most American cities. What I envisage is a dense grid of virtual bus stops in N square miles surrounding a rapid transit stop. You hail using an app, and a minibus (8-20 pax) adjusts its route to collect you and get you to that rapid transit station. The inverse happens for people arriving at that station, where routes are planned as the train approaches, so people heading to the same general area can be directed to the same minibus.