It did fix housing prices in LA. That's why for the past 50 years LA has frozen its zoned capacity which used to be staggeringly high.

The LA metro didn't start construction until 1990. Prices have risen by a factor of 6 since then. Of course they probably would have risen even more but it was obviously inadequate to reduce prices.

While I do agree that land is different, sometimes I think the problem is that people see it as such. When housing markets rise people get rich, just like they do with e.g. stocks. The lack of affordability is a factor of inequality, and especially inequality in opportunities. That is why moving to a smaller cities isn't a solution for most people, because the problem is with opportunities which are appearing in cities and disappearing most everywhere else.

Stock, in principle, is an investment in an enterprise that creates wealth. Like building cars or growing wheat.

Buying and selling houses merely moves wealth around (typically from younger generations to older). It creates nothing, incentivizes nothing and looses more and more to mortgage holders. It can indeed make people rich but only to the degree someone else gets poorer.

The trend is for an ever growing number of single family homes to become rentals owned by investors. As prices rise further and further above middle class ability to afford, this trend will increase. You can make far more money buying a house and renting it than buying it and sitting in it. So in the long term owner-residents are never going to be able to compete for homes with large investor in an unregulated market.