Earlier quoted context omitted.
The change won’t be for free (even though it probably in the end will save us all a lot of money), and unfortunately, everything that cost money will hit the poor hardest. But that is a problem that is solved with progressive taxes and redistribution, not something that should stop us from saving the environment.
The change won't be for free. But rather than lower the usefulness of cars, make sure new cars have better fuel economies (which directly translates to lower pollution). Within 10-15 years, clunkers get replaced anyways, so a general policy of "by 2027, all newly-registered cars must have a maximum amount of X litres per 100 kilometres" or a ban of Diesel engines outside of speciality markets (military, agriculture,…
(Electric cars might be the best alternative in rural and even some suburban areas. But they don't belong in a city.)
The reason diesel engines have been prohibited in certain city centers is because they have been shown particulary bad for people's health [0]. That is usually also something that hits the poorest people hardest. Rich people choose to live somewhere else.
Your last paragraph is just non sequitur. If you want to, you can try to explain why you think that would be the case.
[0] https://www.theguardian.com/environment/2017/may/15/diesel-e...