Name a classical monarchy, tyranny, or republic where the ruler does not have the right/ability to remove cabinet-level members of the government. Even in modern republics this is a standard thing. Pretty sure in modern monarchies most monarchs have the right as well, even if it's not practiced (due to possible protests against -them-).
The ruler should not have to call on the general membership to protest a person out of a position. The person could do an adequate enough job, but the purpose of a cabinet/council is historically to be a trusted group of advisers. i.e. a privy council.
England.
Note the propensity for controversial assassinations of high ecclesiastical authorities. Easier to kill than to remove in some cases.
