Alligator muzzle width

[Hardcastle]

Something that always perplexed me is why do alligators have wider muzzles than other crocodilians?

Everyone always downplays alligators and acts like they are nerfed wussy crocs, but to me the broader muzzle almost looks like an adaptation for struggling with larger prey. The gharial has the narrowest muzzle and we know for sure it's because it only eats fish and couldn't struggle with a large animal, so why does the narrower muzzle of crocodiles and caiman not mean the same in relation to the alligator?

And if it's not that, what is the wide muzzle of the alligator for?

[Methane]

I remember reading something that stated the crocodile's narrower jaws and exposed teeth were better for shearing and slicing prey than the alligator's are. Neither of them can chew, so when they kill large prey, they have to rip off pieces of the carcass and swallow it. Crocodiles are better-adapted for this, however, so they can be more opportunistic in selecting larger prey.
The alligator's jaws are better for grasping and crushing, but not as good at 'shearing', so they're more inclined to aim for smaller animals that don't take as much effort to tear apart.