I hear where you're coming from. But I think it is very dangerous advice.

If you assume that people, especially new managers have way too much to do, and not nearly enough time to do it in...

And if you assume that when people are overloaded and stressed, they fall back to doing what they know best, what they are most comfortable doing...

And if you assume that what former programmers/new managers know best and are most comfortable doing is writing code, not managing their team...

... then you have a real recipe for trouble. I am thinking of one high-profile developent team where I work that promoted engineers into managers, and each time the manager attempted to continue being an active programmer on the team as well, and each time the attempt at management ended horrifically. I saw this happen three times in a row. In at least two of the cases, the "failed manager" went on to become very successful engineering managers with other teams. With no coding responsibilities.

Trying to balance both at the same time can be done, but it's a huge challenge. More than most first-time managers can handle, I would guess.