My armchair solution to this problem is to reform rent control.
The new “affordable housing” rules are an interesting approach to rent control. For the new affordable housing projects, the rent is set at some low price, but only as long as the resident has an income within 2 times the limit to qualify for that rate. And I think the rates adjust over time to account for inflation. Once the resident’s income goes above the limit, then the unit’s rent goes to “market rate.” I heard about this in a presentation hosted by the city, and the city planner said the residents at that point typically have enough money that they want to move to another location, anyway. But this does not apply to pre-1979 properties.
One problem with the equity of rent control and Proposition 13 is that they are not indexed to the income of the resident. Your mother dies and leaves you a house, and you inherit her 1975 tax rate, even if you are a super-rich investment banker. You can’t do much to the property, though, because “new construction” will trigger a reassessment. So, the best thing for you is to rent it out as a low-density rent-controlled slum, and keep the fundamental supply/demand imbalance intact.
It would be good, both for tax revenue and for social justice, for the taxes and rent controls to take into account the resident’s ability to pay. But doing anything to those laws would draw out the NIMBYs like nothing else, and formulas that are too complicated would themselves be an unfair tax.