If you have that kind of density, you can build out and each part of the city is like its own mini city that is perfectly reasonable to live in. If you need to go to another mini city you can bike or jump on public transport.
In Berlin these are refereed to as Kiez for example.
Very large cities don't really have a city center as such, or at least not for most people. And you can have reasonably priced apartments or townhouses in a well connected Kiez that has everything you need to live.
> Did you consider that not everyone has a choice in the matter and the alternative is often unemployment?
And about far more often its the case that people would prefer to live in the city but are forced to live some-where on the far edge and then having to buy a car to drive into the city.
This is what the real problem with the kind of low-density city surrounded by sprawl. The actual city centers are tiny to non existent and lots of cars.