It's not about food, it's about money. There is a black market in exotic meat and animal parts. Live animals too can be poached. Rare reptiles and amphibians and even fish for aquariums. Birds too are poached live.
And of course hunting without a license is like driving without a license. If you don't care about the law because you have no business being here anyway, then violating these laws is a leisurely activity to match your leisurely presence in the US.
I prefer to poach my food in a nice meat stock.