The poorest already don't own or use cars. Getting cars off the road will make buses faster and more reliable, and the poorest will benefit the most from that.

We need fewer cars on the road, so any way you slice it some people have to be pushed out of driving, and any way you slice it the rich will find a way to pay to continue to drive. Either we let them pay directly, and spend that money in public-directed ways that improve transit and help the poor, or we adopt some other system and they'll find more wasteful ways to use money to "solve the problem" that just mean everyone loses out. (e.g. some cities have a rule that each car is only allowed into the city a few days a week depending on its numberplate - so the result is that rich people buy two cars).

> Meanwhile, the people in charge of solving the problem of climate change are still flying around the world on private jets.

And they'll continue to do that until we adopt a carbon tax system so dumb that there's no way around it. But if you try to just "ban private jets" then they'll buy private prop planes, or private trains, or fly around in private full-size airliners...