The conclusion of the article is that there needs to be less parking altogether, not just fewer surface parking lots. Livable places prioritize people, not cars.
I don’t see how you can reduce parking anywhere in the United States, unless you are also talking about building some street cars or some light rail or some train tracks.
The idea is that, if you have neighbourhoods with many things conveniently nearby, people do less "driving to places" and more "making use of neighbourhood features by walking to them."
Every one of those satisfied-demand pedestrians is one less driver out there taking up parking spots (and therefore generating demand for parking lots.)
Sure, that person might still need to own a car for some things (it's still America, some things will still be very far away); and so they'll still need somewhere near where they live to keep a car. But if they need their car for fewer of their daily-life tasks, then they can leave that car at home more. (Or get closer to a car-sharing service being viable for them; or, in a multi-adult family, get closer to downgrading from needing to own two cars, to only needing one.)
