Let's just take your first claim (I don't have all day). Hopefully that's enough to indicate that nothing that you're talking about is the obvious or natural result of basic economic logic, as you seem to think it is.
Point 1: Increase the local tax burden
Your response: "I don't think it's particularly contentious to say that a low-income person paying less in property tax means that a higher income person must pay more in tax to offer the same level of services".
This depends on the assumption that there is a zero-sum competition between rich and poor people. Every X number of poor people in a city, represents a subtraction of an equivalent number of rich people. Because rich people are presumably in a higher tax bracket, they pay more per person that do poor people. But there's no reason to think that there is a zero-sum competition between rich and poor people. That depends on complex empirical questions like the division of labour in the city, the availability of land and housing, if low-skill labour will attract businesses, and so on. And the fact that a poor person might not pay as much in taxes as a rich person does not make them a tax "burden" in any sensible use of that term - they may be net contributors.
I hear what you're saying, but if someone's not paying for the services they're using in taxes, they're a burden being carried by other tax payers. No need to consider land or housing issues or view the whole thing as a zero-sum competition at all. You're bringing in a lot of things that don't really factor into the cost of property taxes at the end of the day.
> Every X number of poor people in a city, represents a subtraction of an equivalent number of rich people
No such logic like this is required - the more people who live in a city but don't contribute their share of taxes, the higher the taxes are for everyone who does. I'm talking strictly about people who are not net contributors - I think you'd be hard pressed to find people in low-income housing projects who are, the housing alone has significant cost and upkeep of it often falls on the city.
That's not to say it has no benefits of course, bringing people out of poverty can be powerful and useful economically, but if I were to state the opposite is true - that we should be decreasing taxes by building more low income housing, you'd look at me like I'm crazy unless I presented some seriously compelling evidence.
You are making your point by definitional fiat, i.e. poor people are people who pay less in taxes than they take (which is not the implication of the statement in your previous post). But it's not at all clear that most people on low incomes do that. You would have to show it.
Point 1: Increase the local tax burden
Your response: "I don't think it's particularly contentious to say that a low-income person paying less in property tax means that a higher income person must pay more in tax to offer the same level of services".
This depends on the assumption that there is a zero-sum competition between rich and poor people. Every X number of poor people in a city, represents a subtraction of an equivalent number of rich people. Because rich people are presumably in a higher tax bracket, they pay more per person that do poor people. But there's no reason to think that there is a zero-sum competition between rich and poor people. That depends on complex empirical questions like the division of labour in the city, the availability of land and housing, if low-skill labour will attract businesses, and so on. And the fact that a poor person might not pay as much in taxes as a rich person does not make them a tax "burden" in any sensible use of that term - they may be net contributors.