Property tax is one way of trying to make sure the people living there care more than a fly's eyes about the property they're being taxed about.

OK, maybe property tax shouldn't be used for education. I can live with that argument.

Someone renting an apartment and who does not (directly) pay a property tax.... what do they care about the (invisible) tax on their (rented) property any more than they care about the (invisible) tax on their income?
To answer that, I have a counter-argument. When I pay my $800 check every six months or so, I damn well care about it. Dammit, make people pay their taxes every three months, six months, whatever and make them SWEAT. When I pay my taxes (and I know I'm unusual, I don't have that folded into my mortgage payment), I see a summary of what is spent toward schools, toward streets, toward sewers, toward the stadium, toward stupid statue at the corner, etc.

If there is no one other thing in favor of it, I favor property tax paying for schools because there are people who are writing checks to pay for it. Direct out-of-pocket expenses invite a LOT closer look than just dumping some state or federal money on it..