There is one argument I've heard against this registry that I think holds water, and that is the privacy concern. The FAA plans to make the drone registration database publicly searchable, and the search results will include owner names and addresses.
It is completely reasonable to conclude that since the FCC database is capable of reverse lookup (rather than by callsign only), the FAA database will do the same. It also reasonable to conclude that as of now, there are far more ham radio operators than drone operators.
I'm not making a case for or against this. I'm just pointing out a federal system in place which already has this.