I would not have stated that the skill set to be a “great engineer” are those to be a “great manager”. Looking back, there was a “do” portion and a “talk about doing” portion of my career, and engineer wea certainly the former. Any form of management, of course, was the latter.

And as basically a hacker, my career choices were easy although the location was damn near uncontrollable.

The most important skill is good rigorous critical thinking which engineering does a great job of developing. You can learn this in other ways - a liberal arts degree can as well, but many of them don't develop it in enough depth.

Management also requires people skills which engineers stereotypical don't have - but many of them do.