You have it backwards. Housing is astronomically expensive in San Francisco precisely because there are so many people with high incomes bidding against each other.

When you have a highly inelastic supply (constrained by zoning laws, density limits, and geographical boundaries), prices rise to the maximum margin of what the highest-income buyers are capable of paying.

Regarding taxes: Since taxes apply to all local high-earners equally, it doesn't change their relative purchasing power against one another in the local housing market. If taxes were suddenly halved, that extra liquidity would be priced into the next bidding war, driving home prices even higher.