Getting people into public transit by making car ownership worse is how you get unhappy people. That is just unproductive and destructive. Make public transit better, that is how you get people out of cars and happy.
> The people that live in the city center probably already use public transit
No they don't. The 74% of The Netherlands lives in a city yet 66% of people commute to work by car. That goes to show that even for people living in cities, going to work by car is still the preferred method. I'm one of them, in the example I gave above it was three times faster to go to work by car.
> because they actually live there, and they will vote them out
That is elitist "fuck you I got mine" mentality. Rich people in city centers able to afford expensive houses will make it harder for poor people in the affordable neighbouring cities to move around and get to work.