Not supporting Public Schools is Child Abuse on a Mass scale.
If you don't like your grocery store, should you try to improve it by continuing to shop there? It seems to me that schools are not going to improve until they see their "customers" going elsewhere. My kids go to public schools, and their classes are mostly just fine. But there are a few atrociously bad teachers, everyone knows they are bad, and yet they keep their job year after year. That needs to change.
I shop at a coop, so yes, I do keep shopping at it even when I'm unhappy with it. I vote in every annual election, and feel free to contact the board when I have concerns. It works the same way with public schools - don't completely disinvest in them, but use the power of the ballot box and communication with publicly-accountable boards.
The analogy with privately-held grocery stores doesn't really apply here, since their board is accountable only for the profit of their shareholders.