"The problem of housing is that regular people want to live in NYC, and Chicago, and LA, and all of these places, and relatively near to where their jobs are"
It's not clear in your phrasing, but it sounds like this is a casual correlation. It's not... Many people only want to live in these cities because it's the ONLY way to get work, given a choice they would quickly move out.
It is a cycle that always leads to increased population density, and has done so since the dawn of agriculture. People tend to go where there are more people, and then work and entertainment happens where most people are, which attracts more people, and so on. This was as true in Ur as it is in NYC.
Or, maybe the jobs are there because people companies want to hire want to live there. We have a way of testing this now given that remote work is a thing. We can see if people would rather work remotely from a cheap house in rural Kansas and have nothing to do in the evenings or live in an expensive apartment in an exciting city where their job is.