We have pet amnesty days here in florida, and have had them for years. They aren't MAKING you hand in animals. It's so you can turn in UNWANTED animals.. and if they ARE illegil, you can't be prosecuted if you're handing them in. So if you were unaware that it was illegil to keep a lion.. and you go hand it in on that day to them, they won't charge you with owning a lion.

If you have a legal exotic, and you can't keep it(or don't want it) anymore, and you haven't found someone to take it, you can take it in to them.

Yes, most will end up euthanized if the zoo(or other organizations) don't take them as exhibits. But it's very preferable to people having animals starve, or be put outside, because they don't feel like caring for them any longer.