That point about context switching most of it to me. A meeting with engineers is so expensive focus time wise. A meeting with managers is just another meeting.
I prefer to think of my manager as my agent. They have my best interest at heart, only want me to succeed, and do the messy work so I can keep focusing at what I’m good at.
My team has as engineering manager and a product manager. I also don’t like being told what to do, but whenever I’m pulled into one of these many meetings for some reason, I’m so grateful to have them
As long as your employer knows you do each task at your full rate, they can deal with the cost. I once had a tech tell me “for $75/hr I will do your shopping for you, and I will do a great job of it. But you probably want me focused on repairing your pool.”