I am not sure exactly at what level you wish there would be more spending on public transportation, but spending money in that field could be a big waste of cash in the US. It's way too big and too decentralized. It makes sense in some countries (in Japan, for example, all cities are on the coast because nobody builds stuff in the mountains, so it's easy to connect the dots), but public transportation would not work well outside of a few big cities in North America.
Even in France, the bullet trains lines cost way too much versus their planned profits. Some will not be profitable for another 20-30 years! And that's assuming that, by then, it's still the best way to get from A to B. It's all about getting votes in the end, it does not make economic sense at all.
You have made a few simple basic errors of data that lead to some very incorrect conclusions.
The bulk of the US population live in areas that have population densities at or even sometimes (NYC) above European levels. The entire state of california (not exactly high density at all, given the bulk of the state is just open space) has an average population density slightly higher than Spain, a country that managed to build a national High speed rail network.
The entire eastern sea-board is at roughly european density levels as well. No one is suggesting we build a bullet train that goes to North Dakota.
As for "not being profitable for another 20-30 years", you are arguing from a very short-term mindset about national infrastructure, but also you are pre-assuming that infrastructure should be directly profitable. This is not a commonly agreed idea, rather there is fierce disagreement between fiscal conservatives who think the government shouldn't do ANYTHING, and those (like most of europe) who believe the government should undertake large "public-good" projects precisely because they are not directly profitable, but they are PUBLIC GOODS.
Universal health care is also "not profitable" directly, but the benefit to society of having everyone live decades longer is massive increased economic output, to say nothing of increased quality of life.
The network effect of having efficient rail transportation balloons the entire economy. This is why governments pay for big infrastructure: everyone benefits and the direct revenue and direct costs are high enough to be uninteresting for investors.
You don't get it. This isn't just about connecting urban centers (which we could, in fact, do a much better job of), it's about getting real, meaningful transit even in places like Los Angeles. Some of these cities rival many countries in population, and have density levels reaching toward Gibraltar.
New York is by far the "shining" beacon of mass transit in the US, but even its infrastructure is deteriorating.
We don't build transit here not because it wouldn't work, but because of purely political factors. It's a punching bag for the anti-tax brigade and the NIMBYs (most also in the anti-tax brigade) go apeshit if they think public transit might bring a brown person to their neighborhood. The horror!
Even in France, the bullet trains lines cost way too much versus their planned profits. Some will not be profitable for another 20-30 years! And that's assuming that, by then, it's still the best way to get from A to B. It's all about getting votes in the end, it does not make economic sense at all.