1. There was a time before cars when all of these issues were handled without cars. God didn’t create cars on day 1.
2. Ask any Floridian about how well cars work when they evacuate for a hurricane. The interstate highways become parking lots.
3. Nobody is suggesting a ban on cars anyway. Individual neighborhoods can be car-free or car-light without any kind of general ban on cars.
The combination of modern day population and climate change exacerbated weathers events (and wildfires), and changes to the landscape, make comparisons / analogies to the past fairly pointless, imho.
I’m not saying there couldn’t be a mix of solutions, but until someone figures out a way to replace the quick “pick up and go with the whole family, pets, and some valuable possessions” capabilities of mass private vehicle ownership, one of the main selling points / purposes of dense, walkable cities is going to be negated imho.
Maybe each 3-4 story apartment building with x number of residents would be required to have on site transportation capable of accommodating all residents, their pets, and some valuable possessions, and they would have to practice emergency evacuations every six months or so.