plenty of places in America could have far better public transportation than they do. Take the Bay Area vs Switzerland

Size: Switzerland 15,940 mi², Bay Area 6,966 mi²

Population: Switzerland 8.85 million, Bay Area 7.76 million

So given that, the bay area is twice as dense as Switzerland

Miles of train tracks: Switzerland 3,241 miles, Bay Area ~300 miles?

SF Bay Area has a bay, Switzerland is all mountains so it's not like Switzerland is particularly easier to cover in public transportation

Plenty of other places in the USA could be covered in trains. LA for example used to have the largest public transit system in the world. It was all torn down between ~1929 and ~1975. A few lines have been created since but, the problem in the USA is, except for maybe NYC and Chicago, public transportation is seen as a handout to poor people instead of the transit the masses use like most saner places. (Most cities in Europe and Asia). Getting it back to that point seems nearly impossible. Building one track at a time, each taking 10-20 years with Nimbys fighting them all the way means the density of tracks always is too small to be useful, and so no usage.

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.