Should the law restrict what animals can be kept as pets?

Obviously everyone on this board is an animal lover and I would hope the type of person who considers getting a new type of animal very carefully to make sure they can meet all its needs and make sure it is happy and healthy. I am not worried about people like this taking on unusual animals (known as exotics in the UK may have different terms used elsewhere) however it seems to me that owners that really do care for animals are actually the least likely to take on "fashionable" species from the start while those who do not do the research and don't care rush in to get their hands on whatever new craze is happening leading to much misery and suffering. This makes me question whether we need stronger legal restrictions on the owning of pets and other animals.

For instance at the moment in the UK meerkats are a big thing. Like everyone else I love the meerkat adverts, and I also love natural meerkats but I appreciate that they do not make good pets. Their needs for social groups of meerkats, to forage and dig, and their personalities are a considerably more bloodthirsty than their cute appearance suggest mean that keeping them is a challenge. Yet they are not restricted as wild or dangerous and anyone with the money can go and buy one (yes just one even though the end result will be a psychotic tormented animal with a shortened life). The same with some types of monkey, birds, other mammals.

Now I am not saying these animals cannot be kept as pets and live happily contented lives interacting with their humans, I am saying that for that to happen the humans have to really care enough to do the research on what the animals need and work hard to provide it. It is bad enough that people can get dogs and cats without any forethought of what being an owner means but as these are already domesticated they have more scope for adapting to poor ownership.

Do you think there should be tighter laws on pet ownership? Should some species be barred from being pets fullstop? What laws would you like to see?