Simply that doing so actually violates the law! The FAA, and by extension the Dept of Transportation, are specifically prohibited by the law they are using to justify this!
Crazy, yes? The FAA and the DOT are using a novel interpretation of this law saying that because the law mentions it that it now falls under their jurisdiction. It doesn't seem to matter to them that it was mentioned specifically as a carve-out, an exemption, and that the vast majority of UAVs will not be flown over state lines for commercial purposes (which is necessary for federalism to kick in).
So if you follow the law, then you would NOT register (unless maybe you are doing commercial flying), as registration is a regulation, and a regulation is NOT a law but a rule that is supposed to have legal authority derived from laws. Over-reach is when a regulation is made that is not lawful, but can still be enforced by the muzzle of a gun and the threat of sanctions (such as jail time or property confiscation).
That's what registration is, over-reach, as this regulatory scheme doesn't have the authority of law.
To give you an example of how this works, as per the FAA website:
"[...] Individuals flying for hobby or recreation are strongly encouraged to follow safety guidelines, which include: [...] Fly below 400 feet and remain clear of surrounding obstacles [...]". Ref:
Model Aircraft Operations
Of course Class G uncontrolled airspace extends from the ground to 1,200ft AGL in most areas, ground to 700ft AGL near airports with towers or FAA weather reports (though the airport itself MAY be in a different, controlled class of airspace), is nonexistent around some Class E airports (case by case basis) and can go up to 14,500 ft MSL over large unpopulated areas.
Ref:
The FAA doesn't control Class G airspace (that's why it's called uncontrolled airspace), so they have no real jurisdiction unless you fly in the wrong area (like over the Whitehouse, or over a controlled airspace airport), or fly too high and end up in a controlled class of airspace such as Class E airspace, or in the Class B airspace of a large international airport for instance.
BUT, if you are an AMA member the AMA limits flight to 400ft. The AMA is a private organization, BTW.
So to be covered by AMA's insurance program included with membership, in the event of a crash you must have been operating within the AMA rules, including the 400ft AGL ceiling! BTW- this insurance covers the aircraft as well as medical for the pilot, and liability as secondary coverage.
But 400ft is neither law nor is it a regulation but merely a guideline, though it is a rule for AMA members (which is a private organization). But if this 400ft rule WERE a regulation, it would be overreach as there is no legal authority for it as airspace has already been classified by law and by treaty.
If you are going to follow the law then you'd stick to Class G airspace for your flights. Which varies based on location, but goes up to at least 700ft or higher where it does exist (which is everywhere except most airports and other flight restricted areas).
So registration will need to clear the hurdle of the courts and is likely to end up at the Supreme Court (which because it IS an exemption would have to rule against the scheme to maintain integrity, there is no grey area here). While this is happening you can bet the DOT and the FAA will be lobbying Congress to give them that authority, so let your Congressman and your Senators know how you feel about that loudly and often!