What income level are you counting as "vulnerable"?
The gap between property taxes and school funding is also quite large (with schools costing far more than property tax brings in): https://www.lincolninst.edu/publications/articles/2022-04-public-schools-property-tax-comparison-education-models
And most food insecurity is covered by federal, not state programs, where the revenue is based mostly on income, which is taxed progressively.