Asians are banned because they're critically endangered in the wild. They're a IUCN Category 1 animal, like black rhinos or other such rare critters. As such, trade in those fish is completely prohibited in the United States as a whole.
Most of the fish on the restricted and conditional lists for Florida are banned because they have the potential to decimate the native populations of fish. Cichlids and payara from equatorial regions in the Amazon can't thrive outside of warmwater canals in southern FL, but fish like ATF and arowanas that can deal with temperate temperatures are much more of a threat, and could be devastating if they got loose. Florida's restrictive, but understandable, laws is a key factor in my decision not to go back there once I'm done with my time in the Army.