But they do? A 4d rotation can be decomposed into a left-isoclinic and right-isoclinic rotation, which in turn can be represented by left- and right-multiplication with unit quaternions.
That's hardly the most straightforward or intuitive decomposition. In particular, it makes simple monoplanar rotations overly complicated, in exchange for making isoclinic rotations super simple--while rotors handle monoplanar rotations entirely naturally, with an obvious extension to isoclinic rotations. And monoplanar rotations are a much nicer primitive to work with.
