> That's a good point you make - even at the extremes of high-density living, high density still doesn't solve affordability!

Manhattan is <23 square miles, containing ~1.6M people, surrounded by a metropolitan area of ~20M. The surrounding metro area has a much lower population density (less than 3% that of Manhattan itself), implying that it's practical for it to be higher, which would reduce housing costs by supply and demand.

It's not about how much housing you have in absolute, it's about how much you have relative to demand. The demand in NYC is about the highest in the country, so they need more supply than they have even now.

> People can neither walk nor bike 80 miles, and public transport over 80 miles with multiple stops takes hours, so you can reasonably expect that prices would be considerably higher in the center (40 miles to everywhere) where it is more desirable, and people can neither walk nor bike 40 miles for commuting. Public transport infrastructure for a 40 mile journey also makes commuting infeasible.

The average commute is 41 miles as it is. And with that level of density you could justify express trains that travel at highway speeds or more, making that distance a much shorter commute than it is even now.

The area in the center might cost more than the outer ring, but what of it? The point is not to make all housing have the same price, it's to build more housing to lower the price of all housing. It doesn't matter if the center costs more than the outskirts if they each cost <25% of what they do now.

It also goes without saying that you would not actually build this. You neither need nor want the entire US population to live in an area the size of Connecticut which represents less than 1% of its land mass; there are multiple metropolitan areas spread all over. The point is merely that enough housing for the entire population would fit in that area, which serves as an upper limit on how much housing demand you could even have. And even Manhattan has a lower population density than we could build at -- it certainly doesn't consist entirely of 100 story buildings despite them being possible to build. The claim that it isn't possible is clearly false.

> The problem of not being able to afford living close to where you need to be is still there, even in the hypothetical pathological case.

That is the pathological worse case scenario because you would have to provide enough housing for a single city with 340M people in it, and you still end up with a lower average commute than people have today.

If you took an existing metropolitan area and raised the population density to that of Manhattan (i.e. lowered the area with the same population) then the San Francisco metro area with 7.8M people would have a radius of less than 6 miles.

And it would be silly to do even that, because all you need to do is convert existing single story housing into multi-story housing and thereby provide enough housing to satisfy demand. You can increase the density by a factor of >50, it's not a question of whether existing construction technology would allow it to be built, but even increasing it by a factor of only 2 or 3 would significantly lower housing costs.