This came up on HN a while ago: https://apenwarr.ca/log/20190926 . The thesis was: "To paraphrase the book, the job of an executive is: to define and enforce culture and values for their whole organization, and to ratify good decisions. That's all. Not to decide. Not to break ties. Not to set strategy. Not to be the expert on every, or any topic. Just to sit in the room while the right people make good decisions in alignment with their values. And if they do, to endorse it. And if they don't, to send them back to try again. There's even an algorithm for this." All of that sounds automatable to me using current or near-future technology.
Managers, especially middle managers, also do many other things; but they universally end up spending a whole lot of time in meetings. I'm not a manager, but my own role in many meetings feels automatable. In a handful of meetings I have to be there because I have detailed knowledge about the subject to share. In the other meetings I think it would honestly be fine for an AI that had learned to emulate my writing and speech to represent me in the conversation and write a summary for me afterward.
I'm not arguing that managers _will_ be automated anytime soon, just that AI probably _could_ automate some of the things that take up a big chunk of managers' time.