I lived in Vancouver, which is very transit friendly by NA standards.
In the residential Neighbourhood I lived in, most roads were 3-4 cars wide, and 2 of those widths were exclusively for parking private cars (parking lane, travel lane, possibly another travel lane, and another parking lane). The building I lived in had as much square footage for parking as it did for living.
Parking a car in was more or less marginally free(as in most North American cities). Using a city parking spot for anything else cost money, and was time limited. Renting a private parking spot was about $100/ month (due to building codes there was an oversupply of private parking in addition to the available street parking). Renting a bedroom the size of a parking spot was $500+/mo.
In other words, the city incentives were set up that a climate controlled parking spot for a car was significantly oversupplied, and cheaper, than a putting a human in the same space.
Problem is: automobile owners chose their houses with these subsidies already accounted for in their budget. Remove them and suddenly it's impossible for them to stay in their home.
Oh, and they can't move closer to the city center: removing the subsidies just made houses that are centrally located impossible to afford for them.
So, spread the change out over a number of years, say 15 or 20. Building public transport won't happen over night either. People can't expect their living situation to stay the same forever, societal change requires personal change too.