The trailer toad will add stability, not take it away, since the trailer ball is located over a set of tires. These aren't new, and have been used successfully is this or similar forms for half a century now.
The trailer toad really only has 3 main drawbacks:
1) Cost
2) Reduced traction. Added weight on the drive axle is certainly needed in some conditions. This would not be a good solution for winter towing.
3) Added steps when backing. It's too bad they don't have an electric locking option.
To a lesser extent, it could also reduce reverse maneuverability since it will scrub the tires in hard turns while backing.
As for legality....
Dollies are legal anyways, and don't require registration when they are empty or towing a registered vehicle. Trailer Toad claims isn't not a dolly, which is probably correct since it's rigidly attached, but either way it wouldn't matter except for maybe charge-by-axle toll roads.
If you want something to fret over... check out many of the home-made trailers being pulled daily on all roads. Many of these have no brakes, questionable structural integrity, and often no safety chains. Seem like at least once a year I see one in the news in my area, for coming off and going through somebody else's windshield. Or the numerous motoromes towing heavy trailers with 2-3x the tongue weight their hitch is rated for, often without the use of any WD at all.