Any permanent solution would require ending homelessness. That's actually a pretty easy goal, but not one our society is willing to pursue.
I think you're also ignoring that we're not out of housing. We're out of housing in the places many people want to live. If you go to Detroit, you can get a house for a song. Alaska will literally pay you for living there.
There's a difference between having a place to live, and living somewhere you want to live. The former is easy to solve, the latter is hard to solve because demand is often driven by exclusivity.
I don't know a single regular on r/landlords who wants that to happen. Just today there was a landlord trying to force a tenant to pay for a window broken by an unaffiliated third party (collateral damage from a neighbor's domestic dispute) when the lease very clearly said the landlord was responsible.
It's trivially true that some can and in fact will climb out of poverty by accepting those N jobs and simultaneously true that most can't climb out of poverty via those jobs alone because multiple people can't accept the same position.
Most of the people who are on the edge of not being able to afford <insert city here> can't all move away into the suburbs let alone Detroit because they can't earn enough money for all the things that aren't cheaper and it would cease to be cheaper as soon as collectively chose to do so. It is only cheap because its undesirable.
You might argue that they should've made better decisions earlier - "my housing is precarious, time to move with my last few bucks before I'm totally out of money" - but then what is your proposed policy for dealing with bad decisions? Do you plan on doing things to try to prevent it? Or try to criminalize bad decisions?
If we want to have people to stop moving to big cities and live wherever they can afford, we need to have the infrastructure to allow people like that to work and socialise. I'd love to buy one of those 1$ houses (although these don't seem to exist as such in Central Europe) and move to some dying industrial town, but if that meant I'd have to work for minimum wage in that one local pub or gas station, and if there were no other people under 50 in a 100km radius, I don't think I'd last long there. I'd rather take my chances in the city.
Nobody owes you a beautiful life.
That's only if you believe that all moral systems are equally valid so whatever the majority wants is right. But I doubt you believe that, because the majority could decide something like "it's okay to rape girls under 15" or "all Jews belong in ovens".
Take a dying area with plentiful houses for cheap move a bunch of people there. It would cease to be cheap and if there is no outside money flowing into an area populated with the poor they wouldn't be able to resolve each others poverty merely by passing the same scant dollars back and forth and pumping each others gas and making each other pancakes. Instead they should all starve together.
You are asking to have your cake and eat it too. Half the nation is fairly poor. They can't ALL simultaneously move to the low rent district and simultaneously take advantage of the lesser cost of living while all working the small modicum of low wages jobs that are fewer in number in total than the number of folks and reorganize America based on this new theory if for no other reason than this relocation by people living paycheck to paycheck costs more than they have and they would tend to in a poorer area descend further yet down the economic ladder as they moved from not being able to afford to live well in <insert city> to not being able to live well enough in <insert poor area> where they have no family or support.
2. It's not about anyone owing anyone anything. You can go to the city and have a small chance at a good life or move to Alaska and have guaranteed survival but nothing more. It's a tradeoff like any other. What it isn't is people rushing to live in a big city out of convenience despite the alternative being just as good otherwise, which is what people often claim - that's what I was talking about.
That's considered an "easy fix" now?
Where I live, the homelessness is seasonal -- they don't stick around for the winters. But when they are here, they subsist by stealing pretty much whatever they can get their hands on. When they relocate, they leave behind immense amounts of refuse. These are not individuals who are down on their luck but tramps who embrace the lifestyle. No functional adult would behave in such a destructive and careless manner.
It is actually incredibly difficult to convince people they should participate in society.