You can solve almost all of those problems more easily by improving road design with knowledge we already have. In relative terms cars are actually amazingly safe given that we drive them trillions of miles a year.
> They're all things that trains and subways provide that cars do not.
Figure out how to get trains to operate everywhere instead of only on fixed routes, and then this comparison will be valid. Until then you're talking about two (more, really) different use cases with a minimal amount of overlap.
So at the very least we will need buses, and a lot of them, to feed the areas where it't uneconomical or otherwise unfeasible to run rails. Do the environmental math on that -- how full does a bus need to be before the pollution per passenger is better than a compact car with one passenger? How about a compact car with four passengers? Public transit would need a fundamental change in approach.
And of course this is only talking about people. Always lost in this conversation is that moving humans from place to place is just one use case.