California, for example, is only slightly less densely populated than France. Nevada is slightly less dense than Norway, but 2.2m of the 3m population live in the Las Vegas Valley, that makes up less than a percent of the total land area, so most of the population live in an area more than dense enough for successful public transit.
There are certainly really low density areas where trains and buses have less utility, but most people don't live there, or they wouldn't have been so low density.
And this is after a century of neglecting public transport. If there was more investment in public transport in the denser areas, density would likely increase further, because public transport hubs tends to drive up footfall to businesses nearby.
Anecdotally, I would claim that a lot more places in Europe with similar density have their density organized around existing city centers, plazas/squares, and other focus points, which makes public transit far more effective. The overall density may be similar (for instance, I live in a major European city and there's farmland next to me) but housing is more concentrated around specific points. Destinations such as grocery stores seem more conveniently located, at least in Switzerland, where every train station and major bus stop seems to have a selection of stores in the immediate vicinity as well as a large amount of housing centered around it, with density decreasing as one moves farther from the transit point.
It doesn't seem like that's the case in the vast majority of the US. While the density of California may be similar to that of France, it seems like people occupy much more of the land.
Here's an article I found that happens to illustrate what I mean, but it unfortunately only has data for a few places: https://www.citylab.com/life/2018/02/theres-a-better-way-to-...
Yet we still had perfectly functioning public transit.
Sure, there are definitive advantages that arise over time once you already have it, such as clustering of shops near transit hubs instead of spread out all over the place, but it still works.
It boils down to willingness to invest. You need to commit to ensuring sufficient frequency and routes for years to change habits even if it operates at a loss.
This is the real problem. You need to be prepared to put the service in before the demand is sufficient to really justify it, because the long term social impact justifies it. Do that, and it shapes the landscape. I mean, the train did that in the US too when it first arrived: entire towns sprung up around access to transit. The convenience of cars would make it harder to cause a reversal, but it's just a matter of which benefits you need to create.
So it's down to political will and lack of public support. The density is a red herring.
As I said, there are quite a few more options nowadays for the last-mile: shared bikes, electric scooters/bicycles, or even Uber/Lyft/rideshare. This should further increase the viability of public transit even in areas of the US in which it wasn't previously viable.
[1]: https://en.wikipedia.org/wiki/Z%C3%BCrich [2]: https://en.wikipedia.org/wiki/List_of_United_States_cities_b...
Electric scooters and e-bikes provide hope of fixing this last mile problem, but they're not yet universal enough.
I think we should laud Tesla and other similar companies for providing a no-compromises solution that results in immediate positive effects on the environment.