You are forgetting that between each row of blades in both Compressor and turbine there are stator blades whose job is to ensure that precisely what you think will happen (rotational motion) does NOT happen.
To put it another way, rotational motion in both Compressor and Turbine gas streams is wasted (rotational) energy.
Partly correct.
The rotational motion only lasts between the aft side of the spinning blade and the entrance to a stator row. However it is within that distance that the heavier particles will deflect outward. Very significant between the back of a fan blade and the inlet to the core.
I believe that there are some patents filed on this very basis (GE, Boeing, etc.)