You can't make statements like that about America in general. Every piece of it has completely different and extremely opinionated housing regulations. Partly as protectionism for the wood homebuilders, so that nobody tries making them in factories.
We used to have factory-built Sears houses though. And now we don't.
Wood houses are cheaper because the lobbying got the other cheap ways to build housing made illegal.
For instance, if you can't build anything more than one story, can't make an apartment, or can't run a corner store out of your house, then it's not productive enough to pay for the construction costs of anything else.
Fire codes are also a lot of it. That's the kind of thing that seems reasonable, then you go back and look at old speeches and they're just saying stuff like "we must make up expensive safety laws for apartments or else black people will move in".
In what countries can you get high quality factory-built housing?
https://en.wikipedia.org/wiki/Sears_Modern_Homes
Currently you can't get them in other countries, if by houses you mean buildings shaped like American houses. That's because we made it illegal to build any other type.
https://www.construction-physics.com/p/japans-skyscraper-fac...
(Also recommend reading everything else he wrote. This is an inaccurate summary of it.)
Also, here's a building in Seattle that's a new type of wood called "mass timber" that can be built very quickly and cheaply. It wasn't legal until recently, and I'm not sure if it is in other cities yet.