Many American cities don't have the population density to make metros and trams economically viable. And those few cities that do have comparable density (New York, Chicago, namely) do have metros.

Public infrastructure has high overhead costs, and low population density means there isn't enough ridership to make it viable.

The problem is when cities treat car infrastructure as absolutely mandatory, and all other transport infrastructure (pedestrian, cycle, bus, tram, train) as optional. When you say that everyone has to be able to get everywhere by car all at the same time, you have to build more roads and parking (at minimum more roads using taxis, self-driving), more roads spread everything farther apart, which means more distance per trip, which means more cars on the road, which means more roads, which means everything is spread farther apart, rinse, repeat.

American cities low density is a direct result of designing for car infrastructure over all else. And car infrastructure is far more expensive than other transportation, and since increased car infrastructure lowers density, it directly makes all other transportation more expensive and less viable.

Since cars are the most dangerous form of transport, for other drives but more so for cycles and pedestrians, it makes it less feasible to use them for your first-last mile. Then you add in that, as the roads grow and distances multiply, speeds are increased to attempt to compensate, multiplying the danger to anyone not in a car.

Rotterdam — a city with a population of around 650,000 — has both a metro and a tram system. Extraordinary density is not a prerequisite.

And in any case, there's no reason that public transit needs to be self-funded. We don't expect the same of most of our other public services.