Deadrose and I used to have a couple of green iguanas; both of them rescues. Local herpetological societies are typically overrun with rescue iguanas, nearly all of them with serious health issues. There was a big brouha here a few years back regarding PetCo's selling of iguanas, and in particular how they sold them as "starter" pets. Yes, iggies are quite personable, almost cat-like, but they require a whole lot of specialized care; and they get big. And if they do get in a bad temper, they have very sharp claws, very sharp teeth, and a very strong tail that they can whip around and cause some serious bruises with.
They are not cheap to care for, they need cages the size of a walk-in closet once they reach full adult size, specialized UV lighting, specific heating and humidity levels, and a specialized diet that can be difficult to provide if you don't have access to a good greengrocer.
As much as I dislike PETAs methods and philosophy, there is one thing I do agree with them on, at least partially. There are some animals that simply should not be kept as pets, period. Every few years there's a big outcry from the exotic pet community regarding some local government bill to bad or restrict the keeping of exotic pets (eg. anything not a dog or cat). As much as I dislike government interference in such matters, I have to say that most of the bills I've seen are not a million miles away from being quite reasonable. The vast majority of the bans are on pets that are difficult to care for or potentially dangerous, or for which there is substantial pressure on wild populations.
Pets like small rodents, small birds, some snakes, and stuff like that is fine. They're relatively easy to care for, and not a huge problem if they get out of hand. But giant snakes (more than 8-9 feet long, 50-60lbs in weight), parrots, iguanas, and so on are simply not appropriate as pets. There are rescue organizations full of these animals, and many more that go mistreated and neglected. And they are extremely difficult to re-home, especially giant snakes. I'd be perfectly happy limiting pet keeping to only fully domesticated animals, with a very few exceptions, or with special licensing.