It’s better than a matrix though. ;) This is like worrying that imaginary numbers are overspecified for representing reals, or that 3D vectors is overspecified

It’s better than a matrix though. ;) This is like worrying that imaginary numbers are overspecified for representing reals, or that 3D vectors is overspecified for representing normal vectors. Quaternions themselves aren’t overspecified, they are naturally 4-dimensional, but it’s true that 3 components is sufficient for an orientation (unit quat). Using quats for orientation is useful in part precisely because of the added dimension - it’s what makes interpolating quaternion orientations better than other representations - you naturally get the minimal and most direct motion. Interpolating any of 3 component orientations doesn’t work as well. So don’t let it irk you, instead find the utility and beauty in the extra dimension.