Great! Repeated studies have shown that most drivers (of anything, bikes included) tend to steer closer to things they are closely scrutinizing, which is exactly what motorists are going to be doing if they're trying to figure out if they are 2 1/2 or 3 feet away from you. One of the first things taught in most competition driving schools is to look through turns, not at the apex, guess why. I sometimes wonder who is ultimately responsible for laws like this. So now if a motorist hits a cyclist, is that prima facie evidence that they were closer than three feet and were therefore breaking the law, thereby rendering their auto insurance contract null and void and ultimately making it harder for an injured/dead cyclist or their estate to recover compensation? I'd rather it be me creating/controlling the separation distance wherever possible, gotta love those sidewalks even more now, and Big Apples to smooth out the joints!
No idea where you got the idea that auto insurance is void if someone was violating a traffic law. In almost all car crashes one or both parties involved were breaking a traffic law - that doesn't make their insurance void, but it does affect whose insurance company will pay for the damages. The 3' law should make it a little easier to recover damages if the driver claims he would have missed you if you hadn't swerved since any witnesses may be able to say that if you swerved at all it was certainly less than 3'.
And the 3' laws don't specify that you should pass at exactly 3', just by at least 3' so there's no need for any close scrutiny of the passing distance, just the realization that you shouldn't be buzzing by someone at high speed without leaving a reasonable amount of room between you.
I don't expect there to be many citations issued as a direct result of this law, but I do hope it improves some driver attitudes through public service announcements and other educational efforts about the minimum passing distance and an emphasis of it in driver training courses for new drivers.