I'm not sure exactly with I agree with the premise that you want your manager to be doing work.
Well, ideally you want your manager to be doing work (rather than not working!) but generally doing a different *type* of work from the people they manage.
In my experience, there are three types of managers. This is a gross generalisation, of course, and they exist along a spectrum in each category - some are poor and some are excellent:
- Those who do at least a reasonably good job of managing work (ie tasks);
- Those who do at least a reasonably good job of managing people; and
- Those who do at least a reasonably good job of managing both.
A lot of managers seem to get promoted to management because they can manage work. Generally, they like work because it doesn't answer back - it can ebb and flow, some of it is urgent and some of it is boring, but once you get used to the type of work it's generally pretty predictable. Work doesn't answer back, it doesn't go and cry in an office, it doesn't take random days off because it's not feeling well, it doesn't complain that John got promoted but I didn't and so on.
Managing people is more difficult because you can't control it as easily. You can't put people aside to wait for tomorrow if they're angry or crying. You need to tailor your approach to individuals, gauge your approach. Some people thrive on it, but most of the managers I have had were pretty poor at it.
The last group, those who are good at managing both tasks and people, is the most elusive group. If you have a manager like that, they should be worth their weight in gold but, unfortunately, it often seems to the Category 1 managers who are promoted.
I agree that your manager doesn't need to be doing the same work as the people they manage, but I do think that it really helps if they understand what that work is, what it involves, and (if necessary) can help out and provide advice. This used to be very common, to my understanding, but over the past 50 years or so, a (probably US-derived) management theory has crept in which says that a manager can manage pretty much anything as management tools and skills are the same. Therefore, in theory you can go from managing a factory making widgets, to managing a callcentre, to managing something else.
So, thanks to places like McKinsey and the proliferation of a plethora of business management courses at universities, we now have a managerial class that are pumped full of management theory and know all about MECEs, Six Sigma, DMAIC and a whole heap of other management tools, but don't actually know about the things they are meant to be using those tools to manage, and don't know how to - or want to - deal with people.