Ironically, LLM’s seem most suited towards replacing many of the functions middle managers perform. But those folks would never allow their own role to be outsourced or automated away.
That's not really the dynamic. If director A used to oversee 3 teams, and she discovers that with AI she can now oversee 6 or 9 teams just as efficiently, she's not going to avoid doing it out solidarity with manager B who's looking for space to move up the ladder.
I'd say it's even more complex. Middle-level management exists because CXOs don't want to deal with their employees but at the same time want them to under control. I don't believe CXOs can trust machines to be as efficient at controlling people as managers. And then CXOs would have to deal with these machines that control people which introduces a new class of problems.