I think the amount of grip the NEA has on schools depends upon the location. I think there are both excellent and atrocious public schools.
You've heard the old saying "A people get the government they deserve"? I tend to think that also holds true in public schools. Schools vary by community and location, and on the whole communities with conservative parents who are concerned about and active in their childrens' education will tend to have conservative, excellent schools.
On the other hand, communities with high rates of disfunctional families will tend to have highly disfunctional schools as well.
JMHO.
Don't kid yourself about the impact of the NEA. They are, I believe, the second largest contributer to the Democratic Party after the American Trial Lawyers. They may not figure in the direct control of the schools where you are, but they certainly set the tone and direction of modern education and curriculum. This says nothing of their extracurricular support for radical agendas across all facets of politcs - and the sacrifice of public dollars to Leftist gods.
Of course, as you say, there are good and bad schools, but on the whole we are in a systemic crisis with education - not an excusable 50/50 dilema. I would strongly disagree, however, with the notion that people get whatever system they deserve. Politics doesn't always work that way. The truth is that what people get for education is something that is often shoved down their throats whether they like it or not. I have heard too many horror stories from relatives, friends and aquaintances to buy the notion that when schooling is failing it is the fault of the parents or that they aren't involve enough. Fact is, many home schoolers become educators because they are sick to death of fighting an entrenched system.
Now, I do not condemn all teachers. In fact, I believe the majority are probably good people trying to do a hard job. It seems to me that the real problems with public education lie in areas like curriculum, spending priorities, theory and pedagogical fashions and the championing of secular values and the like.
I also tend to think that the day of the government run system is over. Government has enough problems tucking in its own fat waistline to continue in the charade of being the right party to mold young minds on top of everything else it fails to do properly.