This method also works well for stock removal from the belly. Just be certain to always split away from the handle, or you will likely split off your handle. That's experience talking.
I can double down on this one! I have wrecked more than once on this road. "THIS time I know what I am doing and I am REALLY being careful.....SON OF A....GAAKAAAHHHHHHH!"
I would be very hesitant to use this technique on the back of a bow. Think about it....you saw down to the edge of the growth ring, but the back of the bow is curved and you have now violated the next ring or rings. And remember, rings are rarely ever consistently thick. Every saw kerf is a chance to find a spot where you have thin rings.
Taking down a stave one ring at a time with a draw knife teaches you how to control your tool, how to finesse a growthring, and best of all it shows you the character of the stave as you get closer and closer to the ring you are going to use as the back of the bow. Frankly, I can have a stave down to the final growth ring a lot faster with a good drawknife faster than you will futzing around with saws, chisels, and a mallet. Do it if it works for you, but stop and wonder why it isn't something everyone already does.