Almost as if comparing NYC 100 years ago to modern Seattle is total nonsense.
Are you really comparing housing standards for the poor today vs 100 years ago? Unless your solution is to throw all poor people in filthy slums like its 1902 I don't see the point of your comment.
Yes, the root problem is population growth. Yes, any organism will continue to reproduce until the population size is constrained by sufficient 'poverty.' The difference is that we are running out of land / unable to keep up with building shelters, rather than running out of food as was common for the rest of history.
Does this mean there are not solutions we should try to enact? E.g. less restrictive zoning? No, of course we should be fighting the problem and realizing there are things we can do in the short term. But, until we get into space and are able to create resources/shelter at an exponential rate faster than potential population explosion, this is not a problem that one "solves" -- only delays/pacifies.
The problem seems to be a sort of network effect in real life. People want to live in cities where there are opportunities. Where are there opportunities? Where lots of people want to live. It'd be an interesting experiment to see a planned city where a large number of individuals/companies agreed, before it was build, to reside there. Bypassing the network effect and ideally make it an instantly desirable location to live. If such an experiment were a success it would create an instantly replicable model that could vastly improve the state of the economy and the country as a whole. But the up front cost of an experiment like this would make something like colonizing Mars seem like the cheap option, even if the costs could be recouped in a fairly short period of time.