Exactly right.
The book I recommended made the recommendation that a move to management always come with a pay cut, and most managers should have someone reporting to them who makes more than they do. I consider both recommendations to be excellent ideas. People should go into management because they think that they are suited to it, and not because it somehow seems like the next step in their natural career progression.
Funny story. Ian Siegal, founder and CEO of ZipRecruiter, first went into management because the programming team told the CEO at CitySearch, "Hey, this junior HTML guy is good with people, we'd rather report to him than the dufuses that you keep hiring as CTO."
Turns out that he was good with people, and was a good manager.