Baking the armature stops the bones from moving...why?

Hi, blender artists :smile: I wish you’re having a good day :smile:

I would like to bake this armature so that I get rid of its parent while keeping the movements of the armature as a whole (location movement). I do this successfully but the animation of each individual bone stops!

Steps that I do:
Select the armature in the object mode > go to Object menu > Animation > Bake Action > check Visual Keying, Clear Parents, Clear Constraints > Click Ok.

Additional info
The armature is the child and it’s parented to the empty sphere. The empty sphere moves along the path using follow path constraints.
The root bone have a Noise modifier on the f-curve. The other bone has a Cycles modifier on the f-curve.
baking tests.blend (601.1 KB)

Your assistance is highly appreciated.