EDIT I am rate-limited so can't reply, but this part:
"If you have 200 cars"
This is only the case if the demand for parking / driving is perfectly inelastic, which would be quite extraordinary. Empirically, when you charge for parking or institute toll roads, traffic tends to fall, in some cases sharply (because many journeys are low value). I repeat: if the parking spaces are still congested, the price should be raised until they're not.
Assuming the number of cars would stay the same is like the lump-of-labour fallacy. Lump of metal fallacy?
Then there's the supply side: guess what, that's not inelastic either! If it's profitable to provide parking, someone will build dedicated facilities for it and charge for their use. This may be an alien concept for some of you, but only because parking minimums cause such oversupply that they can't be run profitably. In cities where parking is priced sanely, it's unremarkable to see this.
"Cars will just overflow into adjacent neighbourhoods" okay, so charge for parking there too, until they don't. Duh.
I don't see why cars should get to sit somewhere rent-free but a human being can't. Urban land is valuable; if you want to occupy it, pay what it costs, ya fuckin welfare queens.
my language is harsh but it's hard not to be when I see so many americans (it's always americans) confidently claiming that life is impossible without free parking. but I live in a city without free parking and things work just fine. I can literally just look out of my window and it disproves all the doomsaying. every commute and trip to the supermarket is uneventful and not ruined in the slightest by a lack of free parking. you pay for parking and it's fine. it's literally just fine. I went to virginia one time, I saw literal acres and acres and acres of empty parking space, oceans of asphalt; nobody seemed to think anything of it but I thought it was mad, like some kind of braindead economic allocation fuckup from a communist country that we'd all laugh about. I wanted to shout: you are being terraformed by asphalt-based lifeforms! why do I have to explain to americans how a free market price mechanism works? on a forum for people to shill their california startups? I shouldn't need to tell you this!