How/Why is it legal to own crocodiles and alligators?

There's a privately owned pet store near where I live, and they often get in baby american alligators and american crocodiles. It surprised me when I first saw them, but they said they're legal to own, and that the state doesn't have a ban on owning exotic reptiles, which include alligators and crocodiles. Even though the state doesn't ban them, they said certain cities may have bans on reptiles in general, but not the city I live in. Doesn't this seem a little weird that Joe Blow could walk into a pet store, buy a crocodile as a baby, and then own this animal that could live well over 100 years which has the capability of mauling it's owners, children, and peoples pets? Don't get me wrong, I don't nessecarily think it should be ILLEGAL to own one, but I think in order to own an animal like this, you should have a permit and you should have the required space that it needs, but here you don't, does anyone else disagree with the selling of crocodiles and alligators to just anybody?