The Ladder Curve is not a concrete thing. It’s a metaphor to explain optimal taxation. It was literally first drawn on a napkin
How does an increase in supply that outpaces demand not lower prices? That’s the question you need to answer.
“Locked into renting” and “affordable housing” have no meaning and are useless terms for discussion.
It’s not a metaphor, it’s as you say, an economic theory for the optimal rate of taxation, which exists somewhere between 0% and 100%. However, in the USA it has been put into practice over the past 30 years, where taxes on the extremely wealthy have fallen drastically over that time, with the thinking being that this would raise government revenue and also all that trickle down hogwash. Only it hasn’t, and it has only served to weaken revenues at the local community and state level, and caused wealth inequality worse than the gilded age.
In terms of housing, you are correct in principle, if the supply of housing was to drastically increase such that it outpaced demand, then sure, prices would fall. But this is a specious argument for a number of reasons. First, even if zoning was abolished tomorrow, it’s impossible to actually build new housing in most of the world’s most expensive cities, such as NYC, London, and LA, because there’s simply no space to build anywhere, except on the extreme periphery. London still has some brownfield land, but LA is boxed in by mountains, and Manhattan literally has no more space because it’s an island. So where do you actually build? Vertically, okay, but then you have destroy existing structures.
Secondly, and perhaps more importantly, even if you allowed easy zoning, and cleared out lots for mega towers, who is going to actually build so much supply so as to flood the market in order to crater prices and make housing affordable? That’s the dumbest thing ever, no builder wants to see prices come down, that would be like DeBeers flooding the market with diamonds, massively increasing supply and dropping the price, and killing their own profits/margins. Builders want high prices, not low, they have no incentive go on a building boom like in 2007 such that prices drop.
So you’re left with my original argument: you can’t leave housing solely to the for-profit, private sector. They have no incentive to build affordable housing, or flood the market with over supply in order to drop prices.