About a third of the people who work in education actually do. Same goes for about a third of the people in law enforcement.
I've spent the last 37 years working in Fortune 500 companies. I've also spent some time working in a very large school system and in law enforcement (probation) in a large city. Large organizations are large organizations, they have similar problems and challenges. The reason? People. All organizations are run by people. Human nature is not defined by a type of organization. Almost every stupid thing I've seen done by a "public" organization, I have seen paralleled in the Fortune 500.
The anti-union propaganda is just that; propaganda. It's all based on anecdotes: "I knew this guy one time", "everybody knows", "I got screwed by a union", while the positive historical benefits of collective bargaining on the US and the rest of the industrialized world have been enormous. The majority of the economies we actually compete with (e.g., Germany, Japan, S. Korea) are more highly unionized than we are. Doesn't seem to hurt their competitiveness.
Employers, (i.e., corporations)all are organized. The owners are collectively represented by management. Why should not the employees form an organization to balance the power of labor vs capital? Historically, when capital holds all the financial and political power, the result is extreme inequality and a large, struggling underclass. History tells us that this will eventually result in an unstable society that will at some point, if not addressed effectively, break out into violence.
Aside from which, it's a stupid argument on the side of capital. Having a big pile of money produces nothing until it is applied to labor. It is labor that produces value. Capital only "capitalizes" on that value to the greater benefit of the capitalist vs the worker who actually produced that wealth.