This isn't really true for any given business. In theory that's how businesses get better, but there are so many examples of businesses doing something horrible for their customers or society at large and then doing nothing to change their internal processes or staff.

I'm not talking about theories about "society at large," because "society" doesn't keep a business in business; paying customers do. "Any given company" with too few paying customers goes out of business, which is an ever-present danger even for companies that try their best. You can treat your paying customers horribly as long as they have no better alternative, as is true of government, union, and other monopoly or near-monopoly situations, or even free market situations where the current crop of competitors are, for the moment, even worse, but companies facing real competition can't do that without losing customers, which is the same as a body losing blood. In a free market, some competitor will figure out how to beat you if your customers don't like you. Even monopolies are of variable durability, and the more poorly you serve your customers (in their opinion), the more people will be looking for a way to provide an alternative and take your customers (and their money).

teachers unions aren't generally opposed to being evaluated at all

No, they aren't generally opposed to being evaluated---as long as they are the ones evaluating themselves. They only object to attempts by "outsiders" to evaluate them.

How exactly are you a customer? What good are buying with your money? I don't consider students to be a commodity, so I'm curious as what exactly you think you are getting.

Too many people in education are confused about this. You are a customer if you are buying something. No, children are not commodities. You don't buy fifty pounds of child per year from a school. You buy education.

Schools are personal service providers like hair stylists. Hair stylists don't sell people, nor do they sell hair. They sell a service that improves people's hair. If you don't like their service, such as insisting that bad stylists can't be fired and you have to take whatever stylist they assign you to, you go somewhere else where, in your opinion, they sell better "hair improvement" service. A hair styling company that acted like the public schools would be put out of business in short order, because they can't afford to pay what the teachers unions pay for political protection of their monopoly.

If education as a service seems like a foreign concept, think of private piano teachers who teach young students. "I don't consider students a commodity" doesn't seem very relevant, yet they are single-subject educational service providers and the schools are multi-subject educational service providers.

And as for what exactly I think I'm getting: Since, strictly speaking, you can't buy skill directly, you buy teaching that creates skill, but you evaluate it by measuring how much added skill is produced, so you are effectively paying for the added skill. To insist that you're not buying skill but teaching would be like saying you're not buying a haircut but the stylist's effort that results in a haircut: meaningless pedantics (that you aren't suggesting, but someone might). If you don't get enough piano skill added to your child for the money you pay, you stop paying the provider and, maybe, look for an alternative provider.

If I put my kid in a private elementary school, I'm still a customer buying knowledge and skills for my kid. I'm just doing a bulk purchase of multiple skills (and including knowing something like world history as a type of "skill").

If I put my kid in a public school, I'm still a paying customer buying knowledge and skills for my kid. The school is still a paid service provider, but in this case, it is one with legislated monopoly power to take my payment from me by force, whether I think their service is worth it or not. Since others without kids are also forced to pay for my kid's education, they are also involuntary customers, but they are buying my kid's education, too.

If my neighbors without kids decided to chip in and pay part of the cost of my kid's piano lessons, they would be customers, too, and would be buying piano-playing skill for my kid. They could be hoping for some benefit for themselves as a result (a source of music for their later years) like a company that pays an external service provider to teach a skill to one of their employees, or it could be altruistic. I'm happy to help pay for the education of a kid whose own parents can't pay. There are things I want to use my money for, and buying useful educations for poor kids is one of them.

But if I, a paying customer, am not getting good enough educational service for those kids from the provider I'm paying and am not allowed to take my money and search for a better provider, I'll be pretty angry about it. Such a situation doesn't benefit my kids or poor kids or customers like my neighbors and me; it merely protects the adults in the politically powerful government-educational industry.