The idea that LA is an unbelievably dense location is puzzling. My Spanish hometown is significantly denser than Los Angeles. Even large parts of NYC are not in any way dense by global urban standards.

As for people parking in the street in the US, you will find them in many smaller cities. Look at random pictures of south St Louis: Plenty of neighborhoods built before every house had a 2 car garage, and therefore with a lot of on-street parking used every day. And that's with single family homes. Hell, you find this in deep suburbs too, where someone decides they want 4 cars, and have the garage full of crap. I could take pictures of at least ten cars parked on the curb, and at least 40 outdoors in driveways if I went for a one mile loop around my 4th ring suburb.

Now, not that this is the main reason Americans still use cars to go anywhere right now, as the rest of the infrastructure around me also makes car mandatory. Suburbs with houses 3 miles from the nearest business, shops inaccessible on foot, streets that, while supposedly crossable, are extremely unsafe to pedestrians... In a world where, say, we limit each household to one car, my entire suburb becomes abandoned, and most businesses collapse, kind of like a place like Madrid collapses if one didn't run any public transit for 4 months.