You're right about empty units in high density properties. It's a problem in a lot of cities (London is another).

I've heard some cities thinking about imposing a supplemental tax on unoccupied housing. It would help a lot, not just in skyscrapers but also in low-density areas where slumlords let their houses rot waiting for the land values to rise.

But unfortunately, the same people who would get hit by this tax are the most solid part of the tax base. Real estate taxes are a huge part of many cities revenue. Increasing them is never popular.