I think “amount of houses” misses many important parts of how people decide where to live and what they struggle with that results in unaffordable or unavailable housing.
Where do you increase supply? The most desirable places to live like urban centers, or more likely more and wider suburbs. In a vacuum many people will say it doesn’t matter and poor people should move to where they can afford; but many people have strong connections to where they grew up and are not inclined to abandon their lifelong support systems because the pricing in one area has gone up.
How do you increase supply? Ugly 5-over-1s are cheap to make but not desirable, not particularly dense. Single family homes are even less dense. Most supply proponents are talking about these or luxury condos.
How much is the new supply? If we build new homes but they are still unattainable to the people who need them, then we didn’t help much right? Which leads me to
Who gets the new supply? Are they put on the open market for speculators/investors/landlords/private equity to gobble up or are there provisions for ensuring the housing goes to people who don’t already have housing or are physically real people not llcs etc.
Tl;dr we could build a million houses but if they are in undesirable places, unfavorable designs, or allowed to be snatched up and resold at the same high prices we already have, then supply alone wouldn’t fix unaffordability of housing across the nation.