In most of the places in the world where there are no "hunter gather types" how is that wildlife population doing. Do you see deer and other wildlife as you drive around, or must you go to a specific place namely an estate belonging to a noble or at the least very rich individual with their permission to see wildlife. I seldom make the 23 mile drive to work or back home without seeing white-tailed deer or wild turkeys, or coyotes, occasionally a bobcat, red fox etc. In my opinion we are still a hunter gatherer society we have simply progressed to a point where we pay others to "hunt" (ranchers, butchers etc.) and "gather" (wheat, corn, soybeans etc.) for us.
As for trying to legally export an alligator, we in the U.S. have had more than a few problems associated with imported animals, and plants becoming rampant and causing problems, so our federal bureaucracy takes steps to avoid helping it happen elsewhere. (Think Snakeheads, Burmese Pythons, Africanized Honeybees, Nutria, Kudzu, Serecia Lespediza, Silver and Bighead Carp, Zebra & Quagga Mussels) Curious as to how you feel about the sudden increase in the population of burmese pythons, and other snakes and reptiles in Florida, should we leave them alone, take steps to eliminate them as much as possible since they are non native, or somewhere in-between?