That includes the currently homeless, and also those who can't afford to live where the rest of their life says they should.
Lack of social safety nets and lack of affordable housing both come from the same root cause, too much greed combined with too little empathy. 'I got mine, time to kick the ladder off the wall.'
>There should be enough housing for everyone that wants to live in a given area, and it should be housing people would want to live in.
The hard part comes in executing, where you have to define “housing people would want to live in (which people?)” and who is in the set of “everyone” whose opinion is gathered about wanting to live in a certain area.
2. "Build more Manhattans" is easier said than done. Even petro-states with astronomical amount of money to splash around have a hard time building a "Manhattan". Dubai might be very shiny and the financial capital of the middle east, but it's no Manhattan.
Back of napkin answer:
Build bigger buildings, lots of them. All of those 'quaint' places with 2-6 story buildings? 50-60+ story sky-scrapers.
However that's probably also the answer you assumed. Yes that would change the 'character' of a place, because the only way of keeping that the same is to keep the number and type of people in a place the same. How could someone preserve an idea that directly contradicts a reality? No, there would need to be a new idea that supports the desired conditions. Hopefully a good idea that is well executed.
As another commenter said, 'more ''Manhattans''' is another way, try to replicate the sort of feel / idea at existing scale or larger in other locations.
My own comment was about the technical and physical goals a society should strive for, which are within reach, should we the people have the will to reach for them.