Not sure if this is a counterpoint, but pretty much every direct manager I've had (except for one, and she was awesome) started their career as a programmer, and I was also a manager that went from programming->management.

While I agree that it's best to have an expert in the field managing you, from my time as a manager I believe the "soft skills" of communication, emotional intelligence, empathy, organization, etc. are much more important. The reason it's so hard to find great engineering managers is that it's difficult to find a "programmer's mind" and a "people-person mind" in the same person.

For one, I think it is extremely difficult to be a manager if you are an introvert. A huge part of your day as a manager is meeting and conversing with other people. If those interactions all take energy from you instead of give energy, it's going to be hugely draining to deal with that much interaction all day. At least that was what it was like for me, so I could just be projecting my experience onto others.