In the US property taxes largely go to fund public schools, local police/fire/emergency medical service, parks, roads, sewer, water, and trash collection.

Generally the amount you need for such services is more a function of how much non-vacant land you have in the area than how much vacant land, so unless switching to just taxing vacant land was accompanied by some tax on something else to cover the aforementioned things it would not work very well.

The fairest system would be a flat tax per person, surely. Each person will use a pretty average amount of state resources. It's expensive to live in California, after all.