Partly that's because in huge parts of the country, it's effectively a necessity to be able to drive in order to get to work, buy groceries, etc., since public transit outside of a few urban cores is very spotty (often nonexistent). Therefore removing someone's license, or not letting them have one in the first place, is seen as a very serious matter that could greatly complicate the person earning a living.
The further east you go, the better it is.
Urban sprawl does make things more difficult, but doing better than the current state would still be quite possible in many cities. For example, taking the two most recent cities I've lived in, Houston and Copenhagen have closer population densities than people may think in the majority of their commute basin. If you draw a circle with radius roughly 30 km from each city's downtown, both have a density of about 1,000/km^2. Yet Copenhagen has 5 commuter rail lines, a subway, and an extensive 24-hour bus network, while Houston has 3 light-rail lines and a pretty bad bus network. So of course it's harder to get around in Houston without a car, even in the dense parts (for example, it's a huge pain to get from a high-rise condo in the Galleria area to an office building downtown, even though these are both dense areas and only about 15km apart). Houston is slowly improving in the past 10 years, though.
Yes, that's true ... but they only just got there. They, or their parents likely grew up in a much more rural, sparser population density.
So in the same way that it's going to take a generation or three to convince folks not to eat as much as a farmer needs to eat to do manual labor all day, it will also take a generation or three to convince folks that they don't need to start an engine to run every errand.
much of american habits, beliefs and culture are heavily derived from rural farming life.
It's anecdotal, but certainly none of the farming background in my family involved car culture. My great-grandfather lived in a small farming town in Kansas, and they didn't own a car. The town, despite being small, was very centralized around a compact "main street" where all the shops were in walking distance of each other, pretty typical of any Midwestern town prior to WW2. People who lived outside of town either rode into town on a horse, took a tractor in, hitched a ride in, or walked. If they needed to go longer distances, they used this method to get to the nearest town with a train station, and took the train. They bought a car when? When they moved to Los Angeles in the 1930s. The rise of car culture and suburbia also led to most of these traditional compact farm towns turning into what you see today, with old downtowns are that are abandoned or semi-abandoned, replaced by a string of strip malls on the bypass freeway—a bypass freeway that in most cases was built in the 1950s or '60s, well after most Americans lived in cities.
Primary reason my coworkers support public transportation, according to them, in an area with pretty good transit (especially for people who commute during "normal" hours): "I want the buses and trains to be good so everyone else will take them and get off of my roads."
Edit: and I dare say people might prefer that after a thorough CBA since it might mean paying $10/day for some private bus service but also saving an hour in commute time while also being able to use the commute to get something else done. But the prospect of tolls that high and riding a bus have a big "ick" factor for a lot of people, so...
Post WW2 government programs encouraged vets and similar to move to the suburbs and highway programs gave way to a very strong automobile industry.
The top it off with more restrictive zoning laws in the US, where compared to Europe you much much less likely to see mixed use of land. in the US land zoned residential is usually kept well separated from industry which does add in commute times and needs for alternative transportation. Throw on that fuel and car taxes have always been cheap
Just by virtue of the fact that you live in the middle of nowhere, should not give you the right to pilot a several ton metal box going 100+kph that has the ability to kill you and those around you.
Driving should still be seen as a privilege and something that you have to earn, not just "oh, you live in the countryside.. well, do as you please"
In many European countries sprawls are illegal. Roads, buildings and public transportation are planned to avoid large low-density cities.