It's not going to be expensive. $10~20 for the license. I think it actually can save the owners' money.
Think about it. Some newbie who don't have a clue decide to get some awesome fish for their look, and he bought ten $150 each saltwater fish plus another $500 for the equipments which make it a total $2,000 investment, then they all died because he had no idea what's going on. It's better for him to be truly qualified before spending all that money.
On the second thought. If all the people are required to have a license agreement before owning a pet, then there won't be millions abandoned pets. Now all the animal shelters can do the administration work for the pet license. All the volunteers can still work there. So no fees for the owner to take the test etc., well maybe just $5 for the photo and the actual license.