The pic of the Type A is wrong.
The type A in the pick is an early No1 MkIII cocking piece.
The type A was similar but more streamlined without knerling around the outer edge and looked similar to a button, but the rest of the profile was the as type B and C.
All sorts of rumors as to why they went to the type B,C but very likely for the same reason they went with the type D to alleviate costs and time of manufacture.