I do think that there is a chicken and egg problem here, and it's part of why we think it's so important to keep poor people in their houses as the place gentrifies; A poor person growing up in a rich city has massively more economic mobility than they'd have growing up in a small town.
Of course, you are right that it's hard to be poor in a big city; but if you can snag a rent controlled room, or your aunt's couch or whatever, it can be a good leg up.
My personal opinion is that if you want to get approval to build an office building, part of that approval would be talking someone into building a similar number of housing units nearby. I mean, not that they should be owned by the same entity; most of us don't want our housing directly contingent on our employment, but you need to build offices and housing in sync, otherwise you get crazy traffic problems.
But they're too damned expensive, and that's a manufactured situation. We intentionally decided that home prices rising faster than inflation is a good thing, and now we get the occasional lip service to "let's make housing more affordable" but _nobody_ has the guts to say "let's make housing CHEAP. Because basic shelter free of indentured servitude is good for humanity". Instead you get "well this building will have 100 market-rate units and 10 affordable ones so we get the odd token normie to assuage the guilt of everyone else living there. But you still get to vote against any meaningful increase in housing supply that addresses the core problem of 1000 people trying to fit in 100 homes."
So, if you make a lot of money, the city is great. If you don't make a lot of money, the city _would_ be great if you could actually afford to live there.