So why not just use Euler axis/angle representations instead? Composition of two rotations in axis/angle representation basically proceeds via the quaternionic

So why not just use Euler axis/angle representations instead? Composition of two rotations in axis/angle representation basically proceeds via the quaternionic formula, ie in terms of half-angles. So if you need to do that a lot, it makes sense to go fully quaternionic to avoid having to work with both full and half angles.