That's why my team has a technical leader role, while I'm an engineering manager. I don't know how much this position makes, but I don't mind if it's more than I do.
I'm sorry you had so many bad managers. But I'll tell you, it's much more than meetings and schedule.

Check out my blog. It's targeted for engineering managers. I've started it after realizing so few of us actually know what they should be doing.

Nice reading! Cheers!