Some origins give more pattern than others, but most shift the story out of the genre. Fantastic gadgets? Science fiction, even if the gee-whiz, pulp-magazine SUPER SCIENCE! type. Likewise aliens from another planet. Urban wizards are urban fantasy. A scattering of powers is almost a hallmark of the genre -- with the emergence continuing over time.
Anyone could acquire a power. Including the children or relatives of an anti-super movement's members -- or the members. True, there would no doubt be envy, but only a strong-willed soul would be willing to say, "Lock me up -- sometimes you need to quarantine the dangerous." Especially since the quarantine would be protection from the danger, not the powers. (And when it turns out that the charismatic leader has super-persuasion powers. . . . )
I suspect most of the opponents will convince themselves that there IS a pattern, and in fact, the super-powered are doing something evil in order to get powers.