Richer areas get less state funding than poorer school districts. These districts have to scramble to just narrow the gap rather than have more funding.
The richer areas have higher scoring schools because wealth correlates with school scores probably due to a combination of natural ability and a more conducive parental and community environment (all multiplicative and compounding over time]. A change in taxes does not affect this one iota.
There are already flat rates paid per parcel in many cities.
There are age over 55 exemptions for certain parcel taxes to raise money for schools.
An income tax per parcel does not scale. How do you tax rentals? Who pays the tax for rentals? What if you want to own multiple homes? What if you are buying a house for your parents to live in?