A classmate of mine had a squirrel monkey and a descented skunk. She brought the skunk in as a prop in some school play. I was doing something with her brother once and went to their house and saw the monkey. He was just sitting on top of a shelf on the wall. As I recall, their parents were somewhat odd, sort of beatnikish.
In the late nineties a monkey lived down the street from us in Brooklyn. I saw it sitting in the window fairly often.
Was just reading this on Wikipedia
So in the 50’s, comic books could have ads for things like dangerous exotic animals, guns, etc, but heaven forbid a toilet tank is on TV!
Most of the ones sold back when in the backs of catalogs/comic books where dwarf caimans. They normally wouldn’t grow beyond 3 feet in length.
I remember those ads. I was very put out that my father wouldn’t let me order one.
An early Mad magazine spoof of those ads went, “Live alligators - surprise your friends! And enemies!”
When I was young my friend down the street wanted a wanted to order a monkey from the comic book. His dad would only allow it if he built a sufficient cage. We spent a lot of time scrounging upmaterals and time building that cage. He got to order his monkey.
It came and his dad helped put it in the cage. When the first feeding time came, a crowd of all of the neighborhood kids gathered. He opened the door a crack and the monkey shot out past him. The monkey climbed the nearest tall tree and stayed there (presumably until he died). My friend wept.
Lead poisoning from leaded gasoline and lead paint is my theory. That and maybe radiation from nuclear testing and shoe store X-rays.
But I think in some cases a little more caution is justified. Letting kids have a potentially dangerous animal like an alligator doesn’t seem like a good idea. It’s also inhumane to let someone get an exotic pet (any pet, really) without some evidence that they know how to care for it.
Exotic pets can also be a problem because people sometimes let them go in an environment where they can live, and create an invasive species problem. Invasive species can cause very real problems- ask an Australian, or ask a Southerner who has had to deal with kudzu.
Anybody want a Wallaby?
Or a married couple sleeping in a double bed!
I was going to ask if you lived down the street from these guys in the '90s, but then I remembered that they actually lived in Manhattan. 
It was evidently a big deal in Psycho as recent as 1960. Pushing the envelope of decency, it was even flushing! Strange days indeed.
As messed up as it is, I think I like the world as it is today better than when I was a kid. The illusions we have to deal with now are somehow more elegant and plausible.
In fact, I remember now that I had an Evil Plan. I did send off for one of those hypnotizing discs. I planned to hypnotize my father into letting me order all sorts of exotic animals that were advertised. Imagine my disappointment when the crappy little disc didn’t work. 
I got the sea monkeys and since I liked bugs of all kinds anyway, I wasn’t too disappointed. When I worked at the zoo we had a number of former pet caimans and a good part of my presentations involved trying to convince the kids that they were not good pets! I actually wore welding gloves to handle them.
The alligators at the Little Rock zoo are fed publicly on Saturdays. Last time I saw, they had a routine where a lady was on the walkway, the alligators swimming around, ready for lunch. She explained that the frozen rats were white, and called to the guy getting the rats that the gators were very interested in her white tennis shoes. 
My kids were watching Friends one night recently, and I said “Why didn’t Mom and I live in an apartment like that when we lived in New York…oh, it was because you had to make a lot of money to afford one.” Our house payment is less than rent on the one bedroom apartment we had in Brooklyn.
I can remember when the Sears Roebuck Catalog sold Shetland Ponies,Sicilian Donkeys and purebred dogs… Never got to order any,tho 
Buying babies?! Mail ordering them from Florida? It really was a different time!
They were a bitch to flush down the toilet when they got too large, too.