You've nailed it. This is why I would go so far as to say that someone with no programming experience can't effectively manage developers.
They rely a lot more on their technical leads to tell them how the other devs are doing at a technical level. They're perfectly capable of managing their professional development without having an in-depth knowledge of enterprise architecture or C#.
So the leads are de facto managers in that they're assisting the manager in managing the other developers. I think this can work, but I don't think it contradicts what I said. It just means the leads wind up doing some managing even though that's not what their titles say.
So, while it's rare there are certainly managers out there who can.
This reminds me strongly on yesterday's Dilbert: http://dilbert.com/strip/2017-02-09
How are the other two points mentioned earlier related to remote working? I am curious.
From what I've seen coding managers seem much more open to remote work than non-coding managers.