There are some parts of the South West Coast Path that you can cycle on and ride your bicycle but most of the South West Coast Path you cannot ride a bicycle on.
The parts of the South West Coast Path that you can cycle on are Braunton to Bideford (North Devon).
All other parts of the South West Coast Path you can only walk it and not cycle it.
The Braunton to Bideford (North Devon) parts of the South West Coast Path are made for bicycles to ride through but the other parts are not made for cyclist and you must only walk through that path.
It becomes dangerous to cycle or ride your bicycle on the walking paths because you can run into people walking down those paths.
So that's why there is no cycling on the other parts of the South West Coast Path because of that.