Not just some, ALL Green Iguanas are from Brazil/Mexico. It's literally Invasive, they aren't from here, aren't supposed to be here.

Yes you are correct; they wreck havoc, and yes they are technically pests by definition, as is anything that causes damage. I think the term 'non-native pest" is more apt. Term pest really undercuts the severity of Iguana problem. Mosquitos are pests also, but they belong, and removal of mosquitos from the ecosystem would cause a collapse. Iguanas don't belong, and their presence in a ecosystem is catastrophic, with their removal actually benefiting the system.

Same with the pythons...These guys are literally destroying an ecosystem. Lots of things are pests, but the effect of Iguanas and pythons on the same ecosystem is very, very different.