I use the drawknife for removing bark, sapwood, and chasing rings. I work quickly with the bevel up for 90% of it, flip it over for finesse around knots, delicate or unusual areas, but then generally put it away, allow it to dry and season, and ultimately progress to cabinet scrapers and sandpaper for the bow's back, and the Nicholson #49, Bowyer's Edge, cabinet scrapers, and then sandpaper for the bow's belly.
No, I don't use cabinet scrapers as my last tool before I finish a bow because it leaves little flats behind and I don't leave flats of any sort on my bows. So I move from them to sandpaper, in progressively finer grades.