I think there is a certain 'magic' in not understanding certain concepts fully. It's probably why I like maths and heavily dislike physics and chemistry. I do not want to make sense of this world. I want to see "the volume of a sphere is 4/3PIr^3" and in some sense see it as an incantation that one would make when casting magic in an RPG. Once you take some calculus, it is a pretty easy formula to derive (integrate?), but there is an allure, an invitation to do some really interesting math just for itself. It fires up our inner curiosity, if you want.
So anyways, I am neither addressing the title's question nor would I really mind if quaternions were replaced in game engines, but I thought it was important to voice the opinion that sometimes it's ok to not understand something.