I've seen both scenarios. Dev managers doing {some percentage of their time} of coding, and a dev manager, doing no coding at all.
The problem is, the more senior you get, the more likely you are to want to be paid more, and the only way to get that in many places is moving into management. (not all of course, but many places). So this can lead to people who are really not prepared to be managers to be stuck in that situation.
(Of course, there are companies where you can move up through Dev, Dev lead - different from Dev manager of course - to positions like Architect etc)
Chances are, being a techy, you may be useless at people-management, plus that takes you further from the code. So you become a bad manager, and are doing less of the stuff you enjoy, and presumably got into development for!
For me, to be a manager you should really be hands off the coding, but absolutely keep yourself uptodate with the technology so you can at least still talk about issues coherently.
As it happens I started freelancing for this exact reason. I have no interest in people management, and I think I wouldn't be particularly good at it, plus I wouldn't get to code as much.