I fail to see how registering drones will help in the majority of cases.
If it just flies around, causing a nuisance and causing aircraft to take avoiding action, then lands again in a field and disappears before it can be reported or found, how is that any easier to trace than unregistered drones.
Unless it has a unique tracking code that is transmitted at all times and can be detected by radar.
Hows about a Mode C transponder, so ATC with an SSR radar can advise aircraft if there is a danger, and TCAS can at least pick it up also.
And if people don't want to pay for the cost of that, then buy a smaller drone that has the controls limited to say 50 metres line of sight, like a remote control toy.