Are you denying that induced demand is a thing for housing? That everyone who wants to move to Seattle will move there regardless of housing prices, and no one will leave because they get squeezed out of the housing market by new arrivals? Or is there a more nuanced argument that I'm missing?
That new condo allows one more family to live in Seattle regardless, whereas if they were competing with existing stock, some family would probably have to leave. We could play a few rounds of musical chairs to prove that fact.
"Squeezing out" is done by a price mechanism: a family that would prefer to stay in Seattle decides to sell, because that new buyer (unable to buy the condo, because it hasn't been built) decides to offer a high enough price to induce the existing family to leave.
That's only done by reducing housing affordability (increasing prices) which is the public policy outcome we're trying to avoid.
It sounds like you agree that new supply is good, I think, because you believe new entrants would otherwise "squeeze out" existing residents and I assume you would agree that this is done by price, and so therefore you would also agree that new housing stock (which decreases the "squeezing") also suppresses price level relative to the alternative fixed stock scenario.
But what you're arguing is different: that increasing supply has no effect at all on the clearing price. That would require an unusual demand "curve" that is perfectly flat, i.e., perfectly elastic, where there is infinite demand at a given price and zero demand at just a dollar above that price (or else that infinite demand would have already pushed prices up higher than the pre-existing price).
This clearly doesn't make any sense for the housing market; home buyers are sensitive to price, there is not infinite demand, some people have more or less desire to pay for a house. In fact, perfectly elastic markets essentially don't exist, and very low slope demand curves only exist in some unusual edge cases in markets (such as commodities that are near-perfect substitutes).
I never argued that it has no effect, only. that it could have no effect. Obviously if you can build enough supply and get way ahead of demand, you will see prices fall. But that just isn't done in practice, so most of the time new supply is brought online, housing prices do not decrease. Well, that's just builders trying not to kill themselves in a market economy, so that shouldn't be surprising.
Thanks to the magic of Simpson's Paradox it is possible to have the average house price go up even if houses get more affordable for literally everyone, which seems to be the situation you're going to. Which is true and interesting, but not really politically important. Obscure mathematical effects do draw attention to the fact that one metric isn't enough to develop policy, but shouldn't eclipse the fact that more houses is what people want, need and should be getting. There is this crowd of people who want to move to Seattle and live in nice houses, let them do that and pay people in Seattle to build them. Otherwise everyone will have to compete for existing housing stock.
We (Seattle) are also completely built, new projects must overwrite existing housing stock and additional capacity only comes from increased density.
If your goal is to decrease costs, the amount of supply needed may be surprising of latent / induced demand is very large. If NYC cost 1/4th the price to live there it would probably triple in population, so you'd need 40 million new units to get the costs down that much, and the price of the penthouse looking at central park would probably increase even if mean and median costs go down a lot. If a city is at the equilibrium point where supply meets demand, more housing may only keep prices flat for a large amount of new housing.
It is only controversial if you really expect prices to fall when new housing is built (or to say, if you think the only solution is to build new housing and nothing else). Otherwise, the "building new housing" part isn't controversial at all.
