One thing I've struggled with is the idea (perhaps a bit old now) that "it's just like having a junior engineer".

I don't really feel that managing a junior engineer is actually an improvement over writing my own code. At least for my own purposes (where satisfaction weighs a bit heavier than productivity).

But that's just me.

But for the people for whom it is an improvement, did you consider that you just got promoted to manager, without an increase in pay?

Because a promotion without increase in pay, is just empty and actually giving you more responsibilities without anything in return.