All that's going to happen in these places is they'll make people miserable as they drive in circles looking for a parking place, or they'll park several streets over, making those neighbors annoyed they can't find a place, then they introduce residential parking permits, to make sure only the right people park.
Eventually home prices and types adjust so that only low income people who can't afford a car park there, or the opposite happens: they knock down a house or two, turn it into a parking lot and rent those spots out, increasing the cost for anyone who wants to live there.
I've lived in a place like that - not having a car was not an option, but it was all apartment buildings with no parking. They gave us a paper with the names of several local places with lots where we could rent a parking spot, which is what we did.
We moved away as soon as we could - who wants to live in a place like that?