Scenario: A high level access account on a single machine, where the account is created by the system/application with a secure password, without exposing the password to a human or to any other machines.
No one knows or can know the password. (Hypothetically the password could be extracted but only if the system is already compromised at the level of access the account has.)
Assume you are watching for and reporting on failed login attempts, you would know if anyone was trying to brute force the password.
The Real scenario where this occurs, the argument is presented that changing the password, could/would raise the risk.
This leads to an argument where there is no good reason to actually change the password on a regular bases. You might want to change it on day one, if you don't trust the random password generation, but even that could add more risk then it removes, as now the password has been seen and processed with human contact.
If no one knows a password, is there a reason to change it?
Note: The example account exists as there is an alternate configuration of this solution, where the account is used to communicate between machines. In the alternate solution the password is known by humans, and shared across devices. The current question is only about the single machine scenario.