1. A lot of high earners want to cram into a small space
2. The existing high earners living in that space don't want to allow more built in that space because they like the neighborhood how it is
So all these high earners compete against each other, and houses become as expensive the winning high-earning bidders can afford.
For this to stop happening, #1 or #2 needs to stop. So, either the high earners need to stop cramming into a small space, or policy must be changed so the locals can't stop the growth of housing supply.
(Usually when I've pointed this out in the past, I get mobbed by NIMBYs who insist that growing the housing supply will somehow cause prices to skyrocket even more. There seems to be a widespread NIMBY belief that standard economics doesn't apply to housing, for mysterious reasons that no one ever quite gets around to explaining. It'll be interesting to see if it happens again today.)
Land at the boundaries of a city is not equivalent with land in the centre, because of location value.
I do agree that #2 should stop, but be warned that it doesn't solve land values going sky-high; it actually increases land values. The solution is land value tax, a la Henry George.
which is what would incentivize the owner of that land (ostensibly a single family home land owner) to sell and let high density to be built. If the land doesn't increase in value this way, the owner would not have any incentive to sell.