Great story. It's always worthwhile to review these powerful, world-changing images. But not all are controversial per se. E.g. the Moore photo depicted exactly what he was on hand to cover. There was no controversy in its creation. On the other hand, Carter took criticism for his seeming detachment from the dying child (though in fact I understand she was rescued moments later).
Forman's falling woman became controversial because of its publication in the Herald, seeming to take advantage of the woman's tragic death. Similar arguments were made wrt Drew's Falling Man.
Galella, of course, inhabited a world of controversy all his own.
Then Brady, as has been pointed out already, drew criticism for arranging scenes prior to photographing them. But I don't believe a photojournalist's code of ethics existed at the time.
To me, Frare's image is perhaps the most powerful, because, in spite of criticism for invading such a private moment, she had obviously earned the trust of Kirby's family to be on hand & document such an agonizing moment.
Hondros took heat for lacking "patriotic discretion" in his photo, &, as you pointed out, Langenberger might have put more interpretation into her image than circumstances warranted—is it possible the bear was old, or sick, or injured?
Demir took criticism for insensitivity in producing the image of the drowned, Syrian-Kurdish boy.
I'm not certain if Nick Ut was ever criticized for his image. Probably. But while it's undoubtedly powerful, I think of it as, along with Moore's, among the least controversial images in the list.
Parenthetically, Kevin Carter took his life after several years of cocaine use, but one strong contributing factor might have his presence along the Bophutatswana border when several Afrikaaners were stopped trying to run past border guards. He produced several powerful images of the survivors begging for their lives, but I understand was caught changing film when guards executed the rest. As a photojournalist myself I haven't experienced situations quite this intense, but I believe that only the lens can protect us from the trauma of these scenes. As far as Carter & the other press were concerned, they might have been executed next. I know I felt horrible for him when I first read about that. Not that he didn't produce other, superb work.
All of these images are powerful, telling & very, very necessary. But they're not all controversial. At least not in the same sense of the word.