The Peter Principle as written about in the book by Laurence Peter and Raymond Hull is that organisations manage careers so that everyone "rises to the level of their incompetence". The paradox derives from the best people at their current jobs are inevitably promoted to the next level, then the next but more often than not they do not have the skills to make themselves successful at the next level up.
Everyone will have at some stage in their careers complained that the best sales-people or best engineers or best lawyers don't make the best managers. The expertise that was so successful at the earlier stages of careers does not translate into managerial ability or leadership acumen. The ability to deliver based on specialised knowledge, being the go to person for having technical knowledge becomes less and less relevant the more senior you get.
The paradox has now been empirically tested for the first time by testing salespeople: https://hbr.org/2018/03/research-do-people-really-get-promoted-to-their-level-of-incompetence
Their results show that:
firms do tend to promote their top sales workers even though they become the worst managers!
So the question is what to do about it?
One option would be to reward the highest producers with more pay but not the promotion, an enlightened approach for sure. I don't know whether that will work in a lot of organisations especially professional services ones as egos and personal ambitions may get in the way.
Another solution is to proactively recognise this paradox and work to make sure the best sales-people (engineers, lawyers etc) are given the support through managerial training, mentoring and leadership coaching that will supply them with the skills they require.
Creating learning environments where the emphasis is on continuously learning throughout people's careers is the key to long-term success and leadership development. With a true learning environment in place and no stigma to taking time away from the day job to learn we could soon have relegated The Peter Principle to the past where it belongs.