Where would you put them? E.g. in the bay area, where you're not allowed to build regular housing and regular apartments to meet the demand, why would they let you build tiny prefab houses?
The problem isn't an inability to construct housing, it's the regulatory capture in the form of bad zoning by home and land owners that prevents the increase of housing supply. We desperately need to fix that, sadly we probably won't until things get much much worse.
There's a lot of empty land in the US ... so, like Oak Ridge and Hanford, there'd have to be new communities, capable of attracting small businesses ... enough to employ the new residents. Some of the first low-cost pre-fabs could be preferentially doled out to people who have have, or want to start a new, small business.
Also ... and I'm thinking of Olympia, WA for example ... government business seems to be fairly stable, and seems to resist recessions quite well. Nice quiet place, for people into that sort of thing.
Nineteenth-century railroads were built in the space of months, if there was a billion feet of wood to be 'harvested'. They didn't cost $10M per mile either. Replace the wood with access to a city 15 or 20 miles away.
It was doable before, and it's just that much more doable.
Even places like Olympia have gotten much much more expensive over the past decade. But we should definitely be doing more to spread the load. As you say railroads are key - Olympia to Seattle on a modern train would be a one hour commute, perfectly within the realm for many people especially those that don’t have to be in the office every day.
But railroads in the US are my biggest pet peeve, we just can’t do them right here. If I had my druthers I’d essentially nationalize the railroads and then hire the Swiss to run them.
That one Oly to Seattle Amtrak that went too fast around the corner makes me sure you're right about our RRs.
Looking back (I'm not much of a rail historian, but) from what I do know, the US rail system was built-out to serve resource exploitation (including populating the mid-continent), not passengers. So personal autos got a leg up on them, in the mid-20s, before they could afford better passenger routes (outside of major inter-city corridors).
I'd guess that if it wasn't for WW2, US passenger rail would have croaked much sooner than it did. The Interstate system didn't help either. AND THEN they were allowed to rip up the old tracks. Ay yay. So clearly some interests were aligned against the RR's. And our atmosphere has and is paying the price.
You also need to put infrastructure in. Depending on how much the population increases, the water, sewage, electric and transportation might need expansion too. And you may need to put in an extra school. And social programs, if you are talking low-income.
Infrastructure scales pretty well with density. You run more miles of pipe to cover less dense regions. Power lines pass more people per mile. Same with fiber.
A single cell tower covers more people.
With enough density that walking out biking is possible, you need fewer highways or subways to move the same number of people. Sidewalks are dirt cheap!
You might be amazed at how the infrastructure costs aren't very high, and with more people you have more sources of income
The problem isn't an inability to construct housing, it's the regulatory capture in the form of bad zoning by home and land owners that prevents the increase of housing supply. We desperately need to fix that, sadly we probably won't until things get much much worse.