Another major counterpoint to that theory: We know well by now that the specifics of the powers are hereditary, though mutating.
Which, by the way, probably explains just why trigger events are so much easier for second-gen parahumans. While their parents had to go through something incredibly upsetting to get the powers in the first place, the kids have mutations of those powers in them all along and just need a trigger event (that matches the powerset, if that is indeed a thing) to unlock them.