I once worked for a shop that went 18 months completely without 'management.' Payroll of around 50, 3 lead men, two secretaries, and a largely absentee owner. We were lacking the shop supervisor and plant manager- who had left under somewhat dramatic circumstances. Sort of made me question the need for most managers.
How long does it take to learn to be an electrician?
Why, then, do we expect a trained electrician to suddenly, magically, become a manager overnight? No coursework, no apprenticeship, no guidance.
Even worse is the trend to having some kid, fresh from school, who's never held a tool in his hand, be hired as 'manager.' These chairborne commandos come out of school, diploma ink still wet, filled with contempt towards the 'ignorant animals' in the field. They have no idea why things need to be done in a certain order, the impact of other trades, or the effort required to learn the skills needed. They don't yet know that you can't master a trade by reading a book about it. Yet, here they come- hired as managers, and they proceed to spend their lives bouncing from one management job to another.
Which brings us to my point: It's not the supervisors' job to "work." It's his job to make sure I can work. That means he doesn't send me to trim out a house before the walls are up; that when I go to that house I have all the parts, help, and tools I need; and that I'm not spending all my time moving stacks of drywall out of my way.
That's why the supervisor needs to know the trade. He has to know what I need in order to function. He need not be the 'best' electrician on the site- but he has to understand what the electrician is doing.