There's a long list of things wrong about this claim.
- A public good does not mean "good for the public." It has a very specific definition: a good where you usually can't exclude people from using and each additional user doesn't diminish the value of the good. National defense is an example. Education is not.
- Even if there are some social benefits to education, the gains from education are largely internalized. If local funding for schools dried up tomorrow, schooling would not cease, not by a long shot. Parents would pay for their kids to go to school. They already do, even though they are also paying for it through taxes. Schooling's so important, they pay for it twice.
- Private education is not strictly for the wealthy. In the poorest parts of the world, the poorest people pay to send their kids to privately run schools.
- Even if the social value of education is high, it also had a negative value. Education (especially higher education) is great for demonstrating intelligence, hard work, and other qualities difficult to observe. Having a high school or college degree shows employers you have those qualities. But when everyone has a degree, then employers can't tell the smarties from the stoners. A dumb person's degree pollutes the value of a smart person's degree.
- Somewhat related, the whole notion of tying education to where you live is bizarre and a recipe for ineptness. Imagine that all haircuts were free, that barbers were paid with local taxes, that legal restrictions made it difficult/impossible to establish new barber shops, and that you could only get your hair cut within a 5 mile radius of where you work.
It is far more logical to send those taxes dollars to flower gardens. These gardens are a public good (it's impractical to exclude people from viewing them, assuming they are in the front yard or other public space; and me enjoying the flowers doesn't prevent you from enjoying them...unless you pick them). The social benefits are high (the person maintaining them receives just a small fraction of the total enjoyment they create), the social costs are low (all I can think of is allergies, and that's a very small addition considering what's already there). And since it's non-excludable, you can't tie a community to a pre-approved set of flower gardens.