Land value taxation makes even less sense for funding local public services. You could build a 500 unit high rise apartment block on a piece of land and pay the same tax as if you had built 10 houses on it.

For schools and policing and the like a poll tax is fair, but regressive. A local income tax on the other hand would rise as the cost of public services rose (since labor is a significant portion of that cost) without being regressive. That would still suffer from richer municipalities collecting more tax and hence having better schools etc. though this could be alleviated with larger (and hence more diverse) municipalities.