You may well be asking why we didn't face any of these problems in the walking motion in the prior lesson. If inverse kinematics is used, the user doesn't rotate the bones directly, and therefore doesn't face the difficulties faced in doing so. The bones are rotated indirectly, using the motion path of the goal object. With IK, you really don't have to think about the rotations of the bones.
Many people do.
For simple swinging arms to accompany a walk, IK is perfect. This is because the entire motion is largely confined to a single plane, just as the stepping movement of the legs is. Put goals on the wrist bones and move simply them back and forth. But for more general animation of the arms, I find IK to be more trouble than it's worth. You can develop an elaborate IK setup, with all kinds of rotational constraints, but even this can be clumsy.