> re people then not able to choose to live somewhere

No, because no such somewhere has been built in the country in question (US) in the past ~60 years, because the default is car-centric. So you're left with a few uber dense, old, predating automobiles, places. Which are extremely expensive, because they simply do not have the capacity for everyone who wants to live in them.

There are plenty of city centers that aren't super-expensive but probably don't have a lot of great local employment options and maybe aren't generally considered desirable--and don't have a lot of great transportation options to outlying areas though that's generally true of a lot of major Tier 1 cities as well. You prioritize your choices.