Axis-angle also doesn't have gimbal lock - the main advantage of quaternions is that actually performing rotations with them only involves addition and multipli

Axis-angle also doesn't have gimbal lock - the main advantage of quaternions is that actually performing rotations with them only involves addition and multiplication, no trigonometry at all. The same is true for using proper rotation matrices, but those use a lot more memory. Plus, you can actually lerp between quaternions (more generally - they compose). That doesn't work with matrices (I think)