I believe Prop 13 forbids the property-value taxes you are suggesting. This is the main reason why cities are not incentivized to build housing. The rather build office buildings, malls, etc. There is just more money in it.
So a new home or a new resident in an old one could pay a tax proportional to the high land value when the transaction happened. Wouldn't that create an incentive to encourage such transactions?
Prior to Proposition 13, the property tax rate throughout California averaged a little less than 3% of market value. Additionally, there were no limits on increases for the tax rate or on individual ad valorem charges. (“Ad valorem” refers to taxes based on the assessed value of property. ) Some properties were reassessed 50% to 100% in just one year and their owners’ property tax bills increased accordingly.
Proposition 13 Tax Reform
Under Proposition 13 tax reform, property tax value was rolled back and frozen at the 1976 assessed value level. Property tax increases on any given property were limited to no more than 2% per year as long as the property was not sold. Once sold, the property was reassessed at 1% of the sale price, and the 2% yearly cap became applicable to future years. This allowed property owners to finally be able to estimate the amount of future property taxes, and determine the maximum amount taxes could increase as long as he or she owned the property.
When the law has become so restrictive that people would rather not engage in commerce at all, then it is broken. This isn't helping anybody.