What's wrong with KISS?
Nowt wrong with that! As I said at the beginning, various methods exist.
However - the method above needs no groundspeed and is flexible enough to give you a quick answer at any time you need to recalculate.
Tain't my idea but it was sold to me by an experienced chief pilot when he saw how I couldn't calculate a new ROD when Roma Control kept us high. I just kind of stuffed the nose down and hoped - then we got too low... I have used it with success ever since. You can use it on any aircraft with a machmeter and it keeps the grey matter working.