How is the Peter Principle relevant to Macbeth?

Macbeth's main problem seems to be that he has risen above his station. He is not fit to be a king.
The Peter Principle was formulated by Dr. Laurence J. Peter and Raymond Hull in their book on management titled The Peter Principle (1969). This is the principle that "in a hierarchy every employee tends to rise to their level of incompetence."
It is common to see people in real life who have been given positions of authority which they are incompetent to fill. Many such people seem subject to delusions of grandeur, even if they are only deputy sheriffs or parking-lot attendants. Their behavior can become laughable.
A good example of the Peter Principle is to be seen in the old movie comedy The Bank Dick (1940). The main character Egbert Souse, played by W. C. Fields, gets a job as an armed guard in a small-town bank. He sees a little boy playing with a cap pistol and sneaks up on him to arrest him with a drawn handgun.
Macbeth first inherited the title of Thane of Glamis. Then he receives a promotion from the grateful King Duncan and becomes Thane of Cawdor. These titles go to his—and his wife's—head. After murdering Duncan, Macbeth becomes the King of Scotland. Macbeth is a good soldier, but not a good king. He has risen to his "level of incompetence." We can see from his behavior even before becoming king that he has many character flaws. He is indecisive, absent-minded, has hallucinations, and is dominated by his wife. He will be feared but not loved like Duncan, who was the rightful monarch. Macbeth is treacherous and vicious. We see his cruel and inconsiderate nature in the way he talks to his servants. He is superstitious, petulant, unpredictable, ill-tempered, and rash. Duncan is portrayed as a gentle, generous, thoughtful ruler who is loved by his subjects, including the man who murders him. Macbeth misgoverns his kingdom so badly that there is chaos, exodus, and rebellion, which he is forced to put down with his brutal soldiers.
Toward the end of the play, Angus pretty well sums up Macbeth's character and the reason for his imminent downfall in these words:
Now does he feel his title
Hang loose about him, like a giant's robe
Upon a dwarfish thief.
It was relatively easy for Macbeth to become king, but impossible for him to retain power because of his incompetence. That seems to be Shakespeare's message.