Greater LA is home to nearly 20 million people. It's entirely feasible to create several car-free neighborhoods, each with more people than Omaha Nebraska. That's plenty enough people for transportation solutions to evolve organically.
Something to keep in mind is the existing suburban infrastructure is also unsustainably expensive. It's quite likely that many American suburbs will decay in the coming decades, a la Detroit, as poor residence can't supply enough tax dollars for maintenance.
I agree with your goals (car free cities), but I don't see this happening. Imagine a neighborhood goes car free - in LA, probably 75+% of people living in that neighborhood work in some other neighborhood. What are they supposed to do to get to work? Public transportation? It doesn't exist, or takes 4x as long as driving.
So we build public transportation up to allow for the massive increase in people using it in that neighborhood? Well, the neighborhoods they're trying to commute to still all use cars, and there's no room for that kind of increase in public transportation there.
So we need some kind of massive public infrastructure project to create the kind of city-wide transportation that's needed to enable this kind of shift? Well, sure. But that takes decades and billions of dollars. And that's if there's the political will to make this happen at all. I live in LA (and commute to another neighborhood to work via public transportation); honestly I don't see it happening.
1) Stop building new roads, and stop improving existing ones. Stop worrying about traffic problems; if people don't like it, they can move somewhere else or start using public transit.
Maybe 1a) Convert some existing highways to toll roads. Use the funds for #2.
2) Use the money saved by not building or widening roads to build and operate more public transit: buses, and especially trains/subways. Give people a way to commute into the city for work without a car.
3) Fix zoning so that higher-density development is allowed, and can't be stopped by NIMBYs. Require mixed-use development where sensible (i.e., retail shops at ground level). Don't require a certain number of parking spaces, perhaps even add a tax for parking (lower for a garage maybe, higher for open lots).
Over time, the area will become denser. People will move closer to the city core, and want to get away from the congestion of the suburbs.
This stuff is perfectly doable, but only if there's the political will to do so. This country simple does not have the political will.
Spend that same money on buses instead.
Instead of millions of cars that carry 1 person to a max of 5, lets have thousands of buses that carry ~40-80 people.
In the years to come when there are less vehicles on the road, we can start closing roads, like Paris does (or did).
Or, you know, do absolutely nothing. Improve nothing. Move forward with nothing. Complain about everything, and every idea to improve stuff.
There are an awful lot of people nay-saying ideas to make stuff better and extraordinarily few people coming up with ideas to make stuff better.
What do you think will be the outcome of that?
That comment even lists a city where they've been successful: Paris
Even if all new construction and city growth is optimized for not needing a car, and a significant fraction of it is, that doesn't change the reality that 300 million people live in areas where a car is an absolute and largely irreplaceable necessity because the existing infrastructure requires it.