The equivalent of polar coordinates in 3d are quaternions. Which do not have gimbal lock, the problem only occurs for euler angles(which should never ever be used for anything ever).
I’d disagree. Quaternions are the 3D equivalent (yes, I’m aware of the subtleties here, but speaking in a rough sense) to using complex numbers to represent rotations.
Euler angles are much closer in spirit to polar coordinates, but unfortunately have gimbal lock.
Compared to 3 numbers and a series of operations which happen to rotate a 3D vector.
Regardless I think euler angles should not be taught except as a dont do this, its a bad idea. Mostly because when used in practice, in order to interpret them you must convert them to quaternion to do so, which is very telling. Gimbal lock is a secondary problem to that.