The geographical disadvantage of the US is probably to blame for this. I don't think that there's a substantial number of rural poor in western Europe.

I don't think that there is any town in Germany that is not reachable by bus, and our inner cities have at least adequate public transit.

Apart from free health care, good public transit could turn some things in the US.

Depends on the city and the job imo. Many cities have very bad late-night bus services (often non-existent), which is a problem if you're a janitor or fast-food worker who gets off at 2am. And many of the better-paying jobs available to the poor are in wealthy suburban areas with bad bus services as well, so with no car you're cutting out a bunch of employment options, like cleaning houses or waiting tables in upscale suburbs. Atlanta has interesting rush-hour traffic along those lines, with a large group of poor people from southern Atlanta driving to jobs in the suburban/exurban counties to the north.