My wife recently went to LA, and between the pictures she sent and me looking into it more afterwards, your description of several cities tied together is a very apt description. Even by what I know (Chicago), LA is just massive.
All of LA was built assuming car ownership. So there are large 4-lane streets everywhere breaking up the usable land. Not to mention huge freeways cutting a net through the whole area. Plus, much of the zoning has segmented regions. You have a whole area just for housing, and another just for commercial property, and another just to industry. So by necessity you need to travel moderately long distances to reach your needed destinations.
I imagine most European cities that weren't built for cars means they originally were built with much narrower and sparse streets, more mixed-use regions, and thus walking or biking a short distance covers the majority of your needs. The rest can be handled by public transportation. In LA, that isn't feasible because so much extra road space means everything is much more spread out.
NYC and other major cities (Chicago) have higher density by building upwards as well as building their public transport from the beginning.
This obviously isn't an overnight project, or even a ten-year project. It would probably take decades to rebuild a car-centric city for affordable housing and walk-ability. It would be easier to start from scratch, for sure. But existing large metro areas have a housing and congestion problem now, so need to start solving it somehow.
China is able to build entire, gigantic, "ghost cities" within a few years. And bulldozers and explosives don't take much time to clear land of existing structures. If there were actual political will to change existing cities to be walkable, it could be done in a very short amount of time.
Low-income people are often the best people to revitalize and area because they don't really have many other options. So the city could take a few blocks of underdeveloped space and have it redeveloped as cheap housing with no parking at all and maybe some nearby retail/office space. People will figure out ways to get around without a car because they have a huge financial incentive to do so.
We've seen this work before. Often times low-income neighborhoods slowly revitalize as people move in because the cost savings is worth dealing with the negative aspects of the neighborhood.