Cities today are orders of magnitude larger (population-wise) than cities in the early 1900s and this is largely due to plumbing and fire codesn Parking is like an afterthought in terms of city planning of any size, usually.
Parking in most US cities is insane because of lobbying and corruption by the car industry. The design challenges aren't unique.
The problem in the US is not size or distance or density, none of those are in any way unique.
The #1 biggest difference between US and other countries is lobbying by car companies. In the US car companies have created not only a plethora of pseudoscientific parking laws but also import/export, safety, transit, and emission laws. None of which make any sense.