Well, yes, in a country that supposes itself the land of equal opportunity, it is unfair to expect your neighborhood schools to be better than everyone else's. If you own a million dollar home, and want your kids to get a better education than public school offers, put them in a private school. Obviously, you can afford it.
And divorcing funding from property taxes doesn't necessarily mean getting rid of local school boards, PTAs, etc. Those institutions, by and large, would remain intact, and just as in control as they are now. As it is now, no one except those who can afford private schools have any choice whatsoever which school their children attend - you live in a school district, your kids attend that school. End of story. And sadly, under the current system, the kids who need the most from their public schools due to poor or nonexistent parenting often receive the least.
I find it a bit disturbing that the people in those higher echelon neighborhoods balk at paying to educate other people's children, but seem to have no problem (and often quite a zest for) paying to prosecute and imprison those same children when they grow up to be criminals.