My biggest problem with these laws is the same problem I have with gun laws and many other laws. It only hurts law abiding citizens. There should be laws (and I believe there are although I don't know details) against animal cruelty whether through ignorance or intent, and laws against allowing an animal you own to harm another person, whether through negligence or intent. I can even see adding some new laws requiring reasonable permits ($200/animal/year isn't reasonable) or other regulation of some species such as tigers or venomous snakes that have potential to be dangerous.
But, people who are knowledgeable about the animals they keep and do take all the necessary precautions to do it safely aren't the problem. Yet they are the ones who are going to get their animals taken away, because they are also the ones who will obey the new law, just like they are the ones already obeying the existing laws. But someone who doesn't care about the law and/or doesn't care about taking proper care of an animal they own and/or doesn't care about making sure a potentially dangerous animal is maintained in a safe and secure manner will still break the law, will still own animals they don't take care of, and will still potentially have those animals end up harming other people. It might be that they go ahead and keep a rattlesnake even though it is illegal and then it gets loose and bites someone (I'm not even going to go into the fact that I think some species of rattlesnakes are native to WV so a rattlesnake bite could happen anyway), or it might just be that they own a dog that is perfectly legal, but it is underfed and under socialized or even deliberately trained to be vicious and the dog ends up mauling someone.
Gun laws don't stop criminals from owning guns and thus they don't stop people being killed by guns. Exotic animal bans aren't going to stop people from being cruel to animals and other people from being hurt by animals.