Just as the parent poster says, the U.S. chooses not to maintain its infrastructure. The infrastructure is not affordable by many municipalities, but that same infrastructure is affordable by U.S. as a whole.
They could subsidize the infrastructure required to integrate the country and keep the non-dense areas viable even if these areas don't have the local tax base to pay for that infrastructure, just as they did with federal highway dollars when they were built, just as many other countries are doing. It's a choice to do so or not. The rules of who pays for maintenance of which parts of infrastructure are essentially arbitrary and the U.S. can alter them if they choose to.
Not from the US, but I lived there shortly and was asked to move there and had to decline. To me it's pretty clear that your single biggest problem is your suburbs and car culture. Everything from anti-social behavior, social anxiety snd isolation, depression, obesity, diabetis, divorce, as well as partisan politics stems from it. Subsidizing that mess should be the last thing you should do.
Other countries subsidize rural areas primarily for 3 reasons:
1. Certain political parties have their base in rural areas and want to subsidize their life style.
2. Strategie for making the country more food-independant through farming.
3. Military strategie for having people in remote areas.
Nobody in the world subsidizes non-productive suburban sprawl.
I think you captured it with "1. Certain political parties have their base in rural areas and want to subsidize their life style."
The suburbs are politically very important in the U.S. because a lot of people live there. The question of most national elections is whether the suburbs will ally with the urban core or the rural areas, and the answer is usually the rural areas.
That's true in some sense, but it's also true that we've built our infrastructure in a way that's very expensive. Car dominance and low-density sprawl don't come cheap.
It's like saying a poor person CAN afford a new iPhone if they just only start eating only rice and beans, and therefore iPhones are affordable for the poor. It's not just about whether the cost can fit the budget, but about what you're getting for that cost.
They could subsidize the infrastructure required to integrate the country and keep the non-dense areas viable even if these areas don't have the local tax base to pay for that infrastructure, just as they did with federal highway dollars when they were built, just as many other countries are doing. It's a choice to do so or not. The rules of who pays for maintenance of which parts of infrastructure are essentially arbitrary and the U.S. can alter them if they choose to.