I think this entire discussion may be somewhat off the mark (concentrating too much of public schools).
Why does tax exist? Because there are services you want the government to offer. And property tax needs to be one of the prongs because a simplistic tax system (income only or sales tax only) are too easy to game. If you no longer want the government to offer those services, vote in the people you want to cut those services.
I will just say that you should spend time in countries where tax is little or nothing to appreciate the difference government services and safety nets make. As an analogy, people grumble all the time about HOA fees. Guess what the buildings look like in countries without them? Run-down, dirty and resale value shot to hell. We are more interdependent than we realize -- the "I don't send my kids to public school so I shouldn't pay property tax" logic is too simplistic.
You're right that we have focused a bit too much on public schools. I'm going to through out a little bit of a theoretical/philosophical argument and see what you guys think. The root need for taxation is to pay for government services. There are a wide range of government services.
Infrastructure and security - roads, bridges, courts, the legal system, customs and immigration, homeland security, and anything like this that make it possible for the nation to produce goods and services. These things provide a return that is enjoyed and used by everyone. Some people enjoy certain parts more than others but in general the nation benefits. For the most part these things are paid for out of the general fund (at each government level. Roads and bridges are often paid for by gas taxes because that at least partly charges more to the higher users.
Generally infrastructure and security are part of the capital stock of the country. It makes sense to me to pay for these out of income tax. In years when GDP and incomes are high we can afford to build to the capital stock. In lean years we should cut back on that. (We'd have cut back now except that the jobs created by building highways and bridges is stimulative.)
Property taxes are collected locally and should be used to build and maintain the local infrastructure. Rich areas with high property values naturally have higher taxes and more money to spend on better infrastructure (including schools.) Since income and sales are dependent on the economy it makes little sense to me to subject infrastructure maintenance funding to the variation.
It seems to me that property taxes should be collected and used to pay for the infrastructure that we need to keep going (though not necessarily add to) regardless of the state of the economy.
Income taxes are a direct tax on current production. It must be recognized that anything funded by income taxes should be on the chopping block during recessions.
Sales taxes charge people for consumption. Similar to income taxes, they should only be used for things that can be cut when times are difficult.
In reality most states and localities fund operations from property and sales taxes. The federal government operates mostly from income taxes.
I don't think our current tax regime in the US is unreasonable. I think most of us would agree that it should be tweaked in many areas but I doubt we could ever agree on exactly how.
The only way to reduce taxes overall and long term is to reduce government spending. That's not a political statement, that's an accounting fact. Whether government is paid for by sales taxes, property taxes, or income taxes really comes down to who you want to pay.
If you are just starting out your consumption is probably high compared to your income as you build your personal infrastructure. A sales tax is the worst thing for you. When you buy a house and finish furnishing it you move on to paying down the debt. You stop consuming so much. Your income rises but your deductions (kids, mortgage interest) do to. An income tax is great for you. Sales taxes are not so bad. But your property taxes on that McMansion might be staggering in comparison
Once you get older, have the mortgage paid off, makes tons of money from salary and investments, you start to like a national sales tax or a flat tax because it would shift the tax burden away from you. After all, you already have everything you need so you won't pay much sales tax. Plus, yachts, luxury cars, private jets, and homes after your third will be exempted from the sales tax because they are stimulative or because the sale takes place in an offshore jurisdiction.