Not grievances, it turns into a legal hassle. I think that the teachers could form professional organizations and get benefits like the NRA has.
At the time of the 50's and before, the NEA was an association of professionals, not a union. They were in a sense regulating themselves as medical doctors or lawyers or dentists did. The NEA was continually working with the states to improve the standards and quality of admission to, and conduct of, the profession.
In the village I lived, if a teacher was found in one of the local bars, or was found to be compromised morally or ethically, his/her employment was terminated, and employment in another district was improbable. Few people today can even begin to understand the civilizing effect that the teachers lent to the average town or small city then. Unionization of teachers wiped that effect out, IMHO.