The distinction kind of matters though. Monopolies are terrible and to be avoided but if you're going to have one, e.g. because roads are a natural monopoly, then you damn well want it to be an elected body and not a for-profit corporation that will do everything it can to extract monopoly rents from everybody in its fiefdom.
Yes they are, this is literally the definition of a corporation. A group of people wanted to form a government to run their "for profit endeavor" so they incorporated, that is, they received a license from their parent public interest corporation(aka "The Government") that allows them to operate under rule of law.
It's corporations all the way down. corporation is really just another word for government.
So in your twisted world view, who are a corporation's citizens? The customers? The surely we should demand that they get democratic voting rights, no?
For the record, my analogy was to describe Apple as a government, not to describe government as a private corporation. I don't think it's in any way "twisted" to describe Apple as the government of the landscape it birthed. And of course people don't get voting rights. It's a benevolent dictatorship open to anyone who considers the terms acceptable. Wouldn't imply otherwise.
I think it's absolutely the case that Sony "governs" the PlayStation ecosystem. That town is way more restrictive than Appletown, but plenty of happy people live there too.
That is basically the definition of communism. communism is one answer to the question "Democracy is supposed to be a good thing for our public governments, why do our for for-profit endeavors not run under democratic means?"
So the communist answer is "fold the manufacturing government into the rest of the government"
Communism has many problems, for one they never actually restore democratic means, to the point that "peoples republic" is sort a joke term for dictatorship. but the one in scope is that running an operation from a large central government will remove the focus a business needs to work well. self-interest is a powerful force multiplier.
In a for profit cooperation the voting rights holders are usually those who have invested in the operation, or them who have bought these voting rights from others. They are usually run as a sort of dictatorship, which does dis-enfranchise the workers, but works very well with small groups.
But the main point was if you want to operate your endeavor as a government instead of as an individual person than it needs to incorporate. The government does not need to be democratic, and it usually is not.
And consider towns, they use the same vocabulary "incorporate" when they want to form a local government.