They are NOT harmless.
About 30 years ago I was renting a house with 3 roommates,
and one of them had a 'pet' iguana - about 3 1/2 feet long the
thing was. He (the roommate) frequently let it out it's cage, and it would
have free run of the house. Granted, it was a large house, but....
Until one day it lunged out from behind a couch and bit someone,
totally unprovoked, on the leg as he was walking by.
It stayed locked in it's cage after that.
Nasty, ill-tempered beasts with a nasty disposition, and sharp pointy teeth.
Not suitable 'pet' material - not at all.
In my opinion they should NOT have 'pampered' invasive
species status. They should remain in their native habitat.
Whatever hell-hole that is.
The teeth of a green iguana are designed to shear plant material, but can deliver a painful bite to people and pets.
https://edis.ifas.ufl.edu/publication/IN528
We were at Las Hades in Manzanillo, Mexico. They have an iguana habitat there. They roam around everywhere. And the ones there are old and huge. They like the pool area and will lay under the recliners by the pool. Didn’t seem to bother anyone else but freaked me out!