Many species of invertebrate would be difficult to import into the US, some expressly forbidden (giant African land snails being a keep example). USDA APHIS very tightly regulates the movement of any species that it deems a potential threat to US agriculture, and the importation or transfer of those species requires a PPQ 526 (because there are so many potential plant predators, there is no "master list" of which species require a permit and which don't, but if a species eats plants, you should assume it's probably on the list). Requirements for this permit include bio-secure facilities, secondary or tertiary containments, plans for the disposal of waste (usually freezing or autoclaving), etc - all to prevent the transfer of insects, larvae, eggs, etc. There's a reason that many "insect" collections in zoos are heavily biased towards tarantulas and scorpions - not only do they have visitor appeal, but, since they don't eat plants and pose no threat to US agriculture, they don't carry the same heavy permit requirements as plant-eating inverts.
Regulated Organism and Soil Permits | Animal and Plant Health Inspection Service
As has been bemoaned on the pages of this site that lament the inability (or at least extreme difficulty) in importing ruminants into the US, agriculture is king, and protecting US agriculture is considered the highest priority by the government.
A few species of plant-eaters which are very well established in the US, such as giant millipede and MH cockroach, don't require these permits.
