I hope you realize this is already the case. Property taxes are voted on locally and go to pay for local schools and there is vehement opposition towards redistributing funding for schools state wide. People move to certain cities where schools are known to be good (and no surprise, those cities also have lots of generous property tax-based and PTA-based funding for schools).
I might add that the people who can afford it move to those certain cities. But yes, you're right, we already do a great job making sure that not all children have equal opportunity.