That's the same with our natives. Can't really own exotics. Besides certain parrots and reptiles with a liscence. We have a state that its illegal to own rabbits/ guinea pigs for that reason. There's a whole fence to keep the rabbits outNative species need a permit or just can't be kept at all. Some states don't allow the keeping of some exotics, like I couldn't keep a lion. But in Texas you could! So it varies by state.
And some states have a list of banned animals because they could become invasive species, like a certain kind of cockroach that's commonly used to feed reptiles isn't allowed in Florida, for example.