Complexity with undefined or difficult to determine benefits is definitely a case against itself.

If you want to charge a newcomer more because the city had to build a sewer treatment plant to accommodate him, you should at least credit him back the ways in which he also made the city more efficient, such as by taking public transit or reducing school costs. And if you are willing to take on the burden of an extensive economic analysis of the marginal cost and benefit of every new housing unit, by all means go ahead. For most of us, a single property tax rate works fine.