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.
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.