I just spent some time with a drawknife and a full size yew stave and had it reduced to bow dimensions in less than 5 minutes. So no, you arent mistaken, the drawknife can remove a lot of wood fast. I almost never use the hatchet. Drawknife works plenty fast for me.
However, Knots in yew wood can really slow your drawknife down, especially if your stave has lots of them. If that is the case, keep a course wood rasp handy or a farrier's rasp and knock the knots down with the rasp between drawknifing.
Last thing, your stave has to be secured so that it does not budge every time you pull the drawknife. A solid bench vise mounted to a solid bench, or a stavemaster bench is great. Stave press is good too.