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

While I can see what you are saying, Puppet; I still disagree with the idea of making more laws that we don't need. PETA already would like us to stop having any pets at all, and believes that they should all be left in the wild. If you find a starving cat, or even an orphaned fawn or a fox, like kfander had; then you would not be allowed to even try and save it.

To give you an example of how that kind of a law would work out, let me tell you about the people who found an orphaned fawn, and they rescued it and took it home.
They knew the fawn needed special attention, so the people took the fawn to an animal rescue that could send it to a facility that cared for and then released orphans like this back into the wild.
Since there was a law against having a wild animal; the police sent a SWAT team to the rescue shelter, traumatized the people working there by threatening them with thier assult rifles, and then the police went into the back, shot and killed the fawn, and carried it out past the rescue workers.
The fact that a wild animal shelter was coming the next day to get the fawn and rehabilitate it for release back into the wild meant nothing to the SWAT team.

I am pretty sure that I posted this story elsewhere on this forum, complete with link to the news article, if you are interested in reading about how laws that were intended to protect the wildlife actually end up getting the helpless animal brutally slaughtered.