Don't know where you live, but to put this into perspective: it's the same situation here and I live in The Netherlands (outside of the major cities). Even in a rich, flat country, the size of a post stamp, we cannot make mass transit work outside of larger cities. I agree that we need mass transit, but it's only one solution for the mobility puzzle. Cars also fit in there as a puzzle piece, especially in areas where the population density is lower.
So from my perspective, no, cars aren't just for the rich.
I agree. The whole existence of a government is based on the union of people to organize common infrastructure that might otherwise not be cost effective to be operated in a commercial manner. Therefore, public transport should be an easy 1, 2, 3. Unfortunately, it's not the reality.