I can see both sides of this, yes by having someone go through a short instructional class to either learn more or just to brush up on how to care for their pet. And the other side to have a license for every pet is going to be hard to implement. The animal shelters here basically ask if you own your home or have the means to take care of your new pet before releasing the animal to you. So in effect they do a small fact check but it's easy to get around it though.
For the exotics and non-native species you should have to go through a class and apply for a license. Now for the fee it shouldn't be too much, maybe the same price as a hunting or fishing license or a few dollars cheaper. Also the animal has to be chipped and if found to be out in the wild and you haven't reported it missing, you can be charged a fine for the retrieval of it.
