Just for comparison purposes, a McDonald's Big Mac weighs 215-240 grams without wrapper, so with a wrapper if you turned a Big Mac into a drone, it would likely require registration.
The real question is, what is their endgame here? Just send out notifications? It isn't like drones have transponders yet(?).
I like the FAA but this seems misguided and unworkable. Plus $5 is significant when some drones this impacts only costs $30.
Hopefully the FAA has birds 250+ grams register too, just for consistency. In particular as birds kill an order of magnitude more pilots than drones have (have drones ever taken down a plane?).