Building new housing usually means also selling the houses, which means a market value assessment, which means more taxes.
Prop 13 only limits tax increases when the ownership doesn't change. The nice thing for municipalities is that even during housing markert downturns, the tax rolls still generally increase every year as those properties with prop 13 valuation caps deeply below the market value still have room to grow when the market value dips significantly.
They are also limited to a total tax of 1%. In most other states, the property tax rate is higher than this, and the income tax rate is lower. With a 1% cap, and a cap on the increase, it's hard for residential taxes to pay for city services. Office buildings require a lot less services, and so they make sense for the city to allow. This isn't the only answer, but it's certainly a major consideration when these things get taken up by city councils and planning commissions.
If a house in the Bay area is $1M and a house in the Midwest is $200k, 1% property tax in the Bay area is about the same as 5% in the other places. Also, be sure to compare tax amounts / ratio to real market value, a lot of jurisdictions say they tax at say 10%, but the tax valuation is always way under market value, so it's confusing.
Either way, it is more expensive to provide services in a high housing cost area, but doesn't scale one to one.
Office buildings are also more likely to never get a reassememt because of corporate ownership shell games that are much harder to do with single family homes.
Prop 13 only limits tax increases when the ownership doesn't change. The nice thing for municipalities is that even during housing markert downturns, the tax rolls still generally increase every year as those properties with prop 13 valuation caps deeply below the market value still have room to grow when the market value dips significantly.