is there a statistic that can show us the density distribution? my intuition says that the bay area would have a pretty gradual slope (people living mostly everywhere of mostly low density), whereas Switzerland would have lots of areas mostly uninhabited while having a few high concentration cities.

looking at the two respective largest cities: Zurich is about twice as densely populated as San Jose.

this has a huge impact on public transit viability.

There are maps

https://luminocity3d.org/WorldPopDen/#8/46.894/7.127

vs

https://luminocity3d.org/WorldPopDen/#8/37.766/-120.721

those are the same zoom level.

I'd argue they show the bay area can sustain far more trains than it currently has.

If you check a Swiss train map you'll see they cover tons of tiny cities.

It's true that Zurich is more dense than San Jose. Some would suggest that's part of the problem. San Jose is less dense because it's missing the public transportation and therefore everyone needs a car, everyone needs places to park that car when shopping, working, sleeping. Everyone is driving to the city so lots of large roads are needed for the cars and so everything expands into car infrastructure. Public transportation enables urban density.