“[i]n time, every post tends to be occupied by an employee who is incompetent to carry out its duties”

The explanation for Peter’s Principle might be NNT‘s concept of fragility: exaggerated reliance on things that worked in the past eventually lead to fragility: the higher management promote individuals according to their PAST performance and those very individuals became more and more self sufficient as they climb up the ladder.
So ‘higher management’ neglect to check if the individual actually has the right qualifications to fulfill his new tasks and the individual neglects to keep on learning new skills as he gets more and more promotions.