I can think of a few solutions* to your counterexample though, and that's the point. There's no reason to expect a solution to be fair in all cases, or perfectly fair in any. I'd only argue that there is often, or perhaps always, a more equitable and direct way to provide for common services than property taxes.
*I choose the BLM as a neighbor purposefully. The rich people in your example would almost certainly prefer to fund their own municipal utility than settle for the type of response I would expect the state or county to provide.
And the unfairness will always over time become skewed towards the wealthy and powerful (municipal authority:'well obviously we are authorized to make exceptions like X as precedented by our rules system in code ZZZ, subparagraph Q; if we give an advantage to corporation Y by implementing change T, it may not necessarily be in the spirit of total fairness - but we will create jobs! and thus it will be in the public interest'). If fairness is your dominant value, the only perfectly fair and sustainable solution is zero. If progressive redistribution is your dominant value, you will wind up with a lot of difficulty over the 'how much is enough' question, and the implementation will almost always find a way to be anti-progressive.
Would you at least agree that things don't have to be quite so complicated once you get out of the city?