All oils have ZDDP in them. Just look at modern engines. They are simply started up and driven away from mile #1. Nothing special is done to them at all.
Maybe all oils have ZDDP in them, but if they do, the level is too low for break-in protection. Modern engines do not need the ZDDP because roller tappets are used, so low friction on the cam and no risk of damage. This is he main reason ZDDP has been significantly reduced from oil...it is no longer necessary.
