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I'm not even sure if this is possible, but I was inspired by this picture.
How could we get alligators and/or crocodiles domesticated? My assumption is that the biggest problem would be finding a niche where they would be useful. Obviously, they can't be used as pack animals. And their meat kind of sucks, so raising them for food is a no-go. Maybe as an auxiliary in battle? Have a bunch of alligators charge in to soften up the enemy's defenses? What about as guard animals for powerful people? Also, which people would be most likely to attempt such a thing? I have an image in my head of alligators in Seminole warpaint charging headlong into Andrew Jackson's army, but obviously that would be ridiculously convergent.