Mongo is correct and how do you enforce the weight of a fish when your told there is a weight needed to catch vs release ? You police it and fine it , its been done in hunting , fishing and so many other sports.
You will have to get a license to fly a drone and register the model at time of purchase like a gun , no exceptions
Another interesting bit of info: The ATF considers the lower receiver of a gun to actually be a firearm. That is the actual part that transfers through the gun shop with the background check. You can order other parts without having to go through the check. For example: The lower receiver of a Colt 1911 (the frame of the pistol) requires a background check because it's the serial numbered part. However, there is no need for the check if you are buying a new barrel and spring. This can be similar to how a model aircraft can be registered. Other parts like the frame, engine, servos, and transmitter can be purchased at a hobby shop. However, the government can require the receiver on the plane to have a serial number and be registered. So yes, there is a way to require registration and a background check for RC model airplanes and drones. The government can even go further if it wishes, and require BOTH the transmitter AND receiver to have MATCHING serial numbers. It can be done if they want it bad enough! But I still have my doubts at this point. Just remember: Never say never.