Quaternions break down for other situations. They cannot represent a rotation greater than 360 degrees. In an engine like Unity (which stores rotation as quats), you can use arbitrary Euler angles in the editor and it will work fine, but the scene file has to store 2 things. There is an additional m_LocalEulerAnglesHint property that covers this edge case.

You're right that quaternions don't work for those. Vec3 is the move IMO. Direction is axis; len is magnitude.