AFAIK many hospitals have a "MBA manager" and a "doctor manager" - I don't know exactly how they relate to one another (who's the "boss boss"), but the idea is that they each bring their part of superior skills to the table.
Would the same idea work for IT? Or, another idea would be, to take a look at how traditional (non-IT) engineering companies work (although the main difference between both medicine and engineering, and IT is that the former are both very high-risk industries that move much slower than IT).
Ive worked at places with a Product Manager and Engineering Manager, at the end of the day after adjusting for company “culture”, product etc what makes a difference is the individual
A good technical manager needs to be able to switch modes - from maker to manager - and back. A person can be a good technical manager even if they don't know the exact technology if they know how to ask good questions of multiple sources and listen (and synthesize) the answers. Nobody teaches this.
Part of it is also that as a programmer you learn to micromanage what the computer is doing, to be very precise with your instructions so the program won't fail. When managing people for the first time the instinct is to do the same: give very precise instructions even an idiot could follow. That's exactly the wrong approach to manage effectively (except for a few rare circumstances). That's why programmers tend to make bad managers who micromanage, they've been trained wrong by their prior work.