A market with more homes per housing seeker is more likely to contain one for you.

As long as that ratio is less than one, some people are excluded. Price is what that looks like in a market. Under central planning it’s typically lotteries and waiting lists.

Supply/demand balance in the region is much more important than the characteristics of any particular unit, and that’s what pro-growth activism is targeting.

It becomes approximately fifo. Oldest or otherwise least desirable housing becomes affordable housing as demand is met with newer more desirable housing being built. But if you're never building new housing, nothing gets pushed out the bottom to become affordable.

That would make sense if location didn’t matter and people couldn’t renovate buildings.

That's just noise as long as construction keeps up with or outpaces demand. The problem is some cities have held back construction for decades, so it will take significant construction to get to the other side of the supply curve.

As a thought experiment, what if you doubled the supply of housing units in Manhattan? Or 10x? 20x? I have a hard time believing housing prices would remain high.

I hate to be the one to tell you, but it's not all about you.