I think you've gotten your definition of progressive muddled. Property taxes are considered to be progressive because property values are widely considered to c

I think you've gotten your definition of progressive muddled. Property taxes are considered to be progressive because property values are widely considered to correlate strongly with income and wealth. Spending those taxes locally (or apportioning funds for local amenaties based on local tax revenue) is regressive, because increased benefit is then therefore correlated strongly with increased wealth and income. Therefore, your example represents a most regressive distribution of tax distribution.