president:
That depends where the engine fails. If you have an engine failure airborne on a normal SID with a 3.3 % requirement you might have the safe choice to stay on the SID and still comply with the required gradient.
True, but irrelevant to performance and engineering. The starting point for computation of the takeoff flight path is an engine failure just above decision speed.
Also, good planning requires a contingency if the engine fails airborne and early into a SID. How do you switch to the preplanned OEI track? Sometimes, that path quickly disappears in mountainous areas. Thus, the reason the U.S. carriers got the FAA to permit the carriers to use a pre-approved carrier-developed departure path instead of using the canned SID. This option is generally limited to airports with challenging terrain.