I think this would take care of a lot of low hanging fruit, but probably not much more. Just like in HAM it is hard to find someone abusing the airwaves unless they are constantly broadcasting (and you can go on a fox hunt. But it is a hunt). So you get the people that are just flying to see the fire and you can ring them up or knock on their door.
The real problem though is that this doesn't fix the major concerns with drone DOS attacks. It is not hard to set up a repeater to control the drone (adding an extra level of difficulty to your fox hunt) or by just programming the drone to take certain actions (even basic AI can do some disastrous things). That seems, to me, to be more what the FAA is after and why more effort is being put in to take down drones instead of tracking the operators. This also has the effect of stopping the DOS attack immediately instead of just fining the person later. This being much more important considering that peoples' lives are at risk.