If cities doubled the number of houses built any year the average price went up by 5% or more, this wouldn’t be a problem.
The tax rate could even be negative.
With how small polities are in the Bay Area this leads this to everyone pushing the burden onto someone else. With a large enough polity responsible for zoning (e.g. New York City's five boroughs) the pressure to add housing becomes too large to completely ignore.
If the government mandates that the price of something is X, and X is higher than the price is now, prices go up.
Also, remember than nominal price and economic price are distinct. “Price” needs to include all tax subsidies and other incentives/ dicincentives.
It might make it sting a bit less buying a single-family home in San Jose for 1.5mil and knowing that you're paying 10x the tax of your next-door neighbors.
Short of massively expanding the poor's ability to vote (making Election Day a holiday, putting it on a weekend, mail-in voting) this holds true in American elections.
My anecdote for the morning.