I don't know how often you buy new refrigerators, but I would rather hire a delivery company every time I change my refrigerator if that means living in a clean city.
On the other car, the ban for private cars usually has only effect during a period of the day. In Barcelona, at least, you can access most streets in the city center after 20:00.
Poor people are probably using public transit, not driving in the first place. Investment in public transportation would be good for them. Investment in roads (automobile infrastructure) benefits only those who can afford cars.
What you say may be true in US cities, or in the countryside.
For me, living in Tokyo, it is really cheaper not owning a car but renting it when I need to, or hiring a delivery service. I guess that the same happens in most major European cities.
On the other car, the ban for private cars usually has only effect during a period of the day. In Barcelona, at least, you can access most streets in the city center after 20:00.