Its even more meaningless to increase property taxes on everyone than to focus the pain into the new construction. a 30k tax on any new unit might be like 10 dollar tax on all units.
The effect of concentrating a tax on something is to make it happen less, and less construction means higher home prices and higher rentals. San Francisco needs to build 1000 units to bring rental prices down 50 bucks. What you need is not to punish, but to make people responsible for the infrastructure they use, and everyone is responsible for the usage, and new construction even less so: until the building is used, the increased infrastructure usage is less. And once its built, all the dwellers pay sales tax and income taxes as well. They will be brining more than their fair share.
Perhaps you believe that the new construction represent a minority that can be exploited, after all, they found a way to profit from the city. But the ones that exploit it the most are the state and the current residents. SF has one of the highest budgets in the world, per city per inhabitant. It doesnt need more money, it needs more discipline.
But there you have the actual issue of SF and california, things like prop 13 that make it impossible to raise taxes on property owners but it makes it easy to apply sales taxes which are known and accepted to be regressive.