That is not the argument. In your example, demand is increasing more than supply, so obviously prices would not fall.
Supply has to increase at a rate greater than demand (including higher property taxes to incentivize sellers to increase supply of properties for sale).
Traffic lanes work this way, notoriously. It’s also fundamentally one of the mechanisms underlying Jevons Paradox.
https://en.m.wikipedia.org/wiki/Induced_demand
Again, the practical example in real estate is Colorado mountain towns. Demand, supply, and prices all accelerate together, and this is particularly amplified because of the customer base in question not having any real price sensitivity etc, and then driving out the portions of the market which do have price sensitivity.
Like it or not, induced demand is a very real phenomenon, and in real estate and similar markets it observably does not always occur at a lesser price due to other positive feedback loops being induced. And you cannot “peel away” those effects separately - the price increase will not necessarily occur exogenously without the demand induction and vice versa.
Again, you’re trying to pick apart the “but that’s separate from the supply increase!” and unfortunately that’s not really severable. The demand increase wouldn’t have occurred without the supply increase. Jevons Paradox being real doesn’t mean gas prices will never go up, so to speak.
Induced demand is a specious argument because the demand is not actually induced by the new construction, it's suppressed by its absence.
If you have traffic congestion, or a housing shortage, then people who would have used the road or moved to the city instead do something else. The normal amount of demand that would exist in a functioning system is suppressed.
If you then alleviate some of the shortfall, that demand comes back. But you haven't induced it, you've just stopped suppressing it through congestion or high prices.
The most important thing about this is that the amount of demand at the lower cost isn't infinite. It's just more than there is at the higher cost. What this means is that you thought you had a shortfall of 100,000 units but you actually had a shortfall of 250,000 units. What it doesn't mean is that you can't solve the problem by building more units -- you just have to build 250,000 rather than 100,000.
This is not a practical example because Colorado mountain towns are not fungible or reproducible. This applies to much of the western US that features amenities in very limited supply that cannot be increased, such as low humidity, tall mountains, surfing, and vast expanses of public land. So the US west will always be expensive, especially if you have an airport/Costco/Apple/Trader Joes nearby.
NYC has a similar dynamic, since no other US city will come close to having a comparable subway transit system.
But this would not apply to places that are relatively fungible and in greater supply, which include many metros in the southeast/midwest/northeast.
Induced demand is a thing, but the population of people is limited hence total demand is limited.
I don't think that's the fundamental/underlying dysfunction of the real-estate market, because the same induced-demand effects clearly exist in other areas. Again, things like Bitcoin pretty clearly demonstrate that supply can induce its own demand and then build a positive-feedback loop that would not have existed exogenously.
But regardless, it's equally true of the real-estate that both grandparent and I were talking about. If induced demand doesn't count because every real-estate parcel is a unique good, then you also can't ever compute a curve for price, because supply will never exceed n=1 either. Therefore the Law Of Supply and Law Of Demand do not exist in this universe and GP's assertions are still false.
I'm not sure that's a useful way to think about the world, clearly real-estate is at least somewhat fungible (people don't not buy an apartment because they lost a single bid) but if you want to use that model, grandparent's arguments are equally broken, for whatever value of broken you are asserting here.
The more useful analysis imo is that real estate is mostly actually not about real estate - it’s about community, economy, etc. And those are clearly things that are highly susceptible to induced demand. There is a near-infinite supply of beautiful mountain slopes, but that’s not really what people are buying homes in Vale or Breckenridge for. They are buying it for the social factors, which is effectively 100% pure induced demand in this context.
And what would happen to prices in the new area if you kept building, instead of stopping? Finding an inflection point in the curve and passing legislation forcing everybody to live inside it is no proof that there isn't a point higher on the curve where more supply reduces prices again.
