A company could do that, but what advantage is there to doing that over simply keeping stage A a secret? By patenting stage A, you are awarded a temporary monop

A company could do that, but what advantage is there to doing that over simply keeping stage A a secret? By patenting stage A, you are awarded a temporary monopoly over stage A but also giving competitors a head start to reverse engineer stage B. By not patenting stage A, you don't get the temporary monopoly, but you also don't publicize anything about stage A that would give competitors the head start on stage B. So it's the same tradeoff that always exists with patents.