The premise is that as long as the monopoly business is not engaging in unethical business practices that it doesn't matter if they're a monopoly. All ancap ideology focuses on is barring the unjustified use of force or fraud in interpersonal relations. As long as a big company doesn't break those rules, then they can only maintain monopoly status by doing a fantastic job such that nobody sees an opportunity to compete with them or is able to successfully compete with them. That's perfectly ok in ancap world.
The premise is that as long as the monopoly business is not engaging in unethical business practices that it doesn't matter if they're a monopoly. All ancap ideology focuses on is barring the unjustified use of force or fraud in interpersonal relations. As long as a big company doesn't break those rules, then they can only maintain monopoly status by doing a fantastic job such that nobody sees an opportunity to compete with them or is able to successfully compete with them. That's perfectly ok in ancap world.