I don't see the problem here. You aren't entitled to ownership of multiple houses. Being forced to sell one house in order to buy another one sounds like working as intended to me.

But that’s entirely my point. It’s hard to actually realize these gains in practice since when you sell your house, the increase in value is absorbed by buying your next residence, which has on average also inflated in value.

Unless you move somewhere the cost of living isn't crazy, and pocket the difference.

That’s a one-time trick, and it only really works if you were already wealthy enough to own in a HCOL area to begin with.

Plus “moving to a less desirable area” doesn’t really dovetail with most people’s assumption of “increased personal wealth”. It is sometimes a good option for retiring somewhere cheap, which absolutely reflects a real increase in net worth. But it’s far from liquid worth and requires steep compromises not everyone is a fan of.

My point was that "rent it out and print money" doesn't always work. I did it with a home I owned, but that was also a period of time where I was a) bouncing around the country renting the roof over my own head and b) waiting to sell after taking it in the shorts value-wise during the Great Recession. I was never underwater, but would have taken a huge capital loss for awhile if I'd sold.

You aren't entitled to ownership of a single house, either.

This is an English sentence with grammatical structure, yet no coherent meaning.

If I can be approved for a mortgage or have cash on hand, and have someone agree to sell me a house, and I sign a contract with them to purchase said house on such-and-such a date, and I fulfill my end of the deal and don't default on the contract, then yes, I am entitled to ownership of a single house. Because I bought it fair and square, and it's now legally mine. Just like if I were to stop making payments on said house, the bank would then seize it, and then I wouldn't be entitled to own that house any more, because I defaulted. This is not rocket science.