I think there's a misunderstanding. I'm not claiming that parking space if charged at the market rate for an unimproved cement room in a high rise is particularly cheap. You can only fit so many cars within the footprint of a typical condo after all.

I'm claiming that removing parking (ie converting the raw sq footage over to living space) would not meaningfully impact housing prices. The existence of parking, free or otherwise, is not a significant contributor to the housing shortage. The issue is one of scale. That's what my "drop in the bucket" comment is referring to.

You specifically said "American housing prices and rents are increased to pay for them". That is technically correct but in context it is blatantly wrong. The price increase as it stands is approximately zero.

The error is failing to differentiate between cost due to construction and maintenance versus cost due to land value. The latter is linked to total supply and thus height restrictions. The former is not the primary component in HCoL cities. You can easily verify this by checking the cost to purchase an apartment building in say San Francisco versus a small town in the midwest. (I refer to the cost to purchase the entire building there, not the cost to rent a single unit.)