If it's your gun, why shouldn't you be liable for harm committed with it? Shouldn't you as the owner be responsible for ensuring the gun is safely stored, and duly reported when lost, stolen or transferred?
That's simply a matter of taking responsibility. And no, it is not an infringement on your right to be legally responsible for the harm caused by the dangerous implements you choose to own.
What makes you think the hundreds of millions of firearms in this country aren't generally owned by responsible people who store them adequately? Those committing mayhem and personal injury overwhelmingly do so intentionally, and will not be the least bit hampered by any laws, because they are already hell-bent on breaking them.
All you propose in an increase in the layers of infringement of the RKBA for people who are already doing things right. The number of accidental shootings in paltry in comparison to those done of malice and with with forethought by people who will neither register nor insure their weapons.
If someone fails to insure their vehicle, I am not the one who should have to pay for the damage they do with it illegally, nor should my vehicle insurance company have to pay for the liability for the actions of another. What you propose is only a camel's nose under the tent, because it will be ineffective, anyway (even if everyone would go for it), and from there the tinkering with the measure to further infringe upon the Right would begin. We have seen that strategy already. It is how the health care system was "fixed" and will likely never be as great as it was unless that ACA crap is stripped out, root and branch, as we were told it would be. If we can't trust our own liars in Government to perform the signature tasks which led to their election, how in the Hell can we trust anyone in Government to look out for our Rights? The simple answer is that we can't. Power corrupts, and it is ever more evident.
The only counter to that power, usurped above and beyond the limitations of the Constitution by twisted interpretation of the SCOTUS, is the overwhelming force of Americans, who by benefit of being Armed and even without martial training represent the only serious balancing deterrent to the corruption in Government. Consider it a two hundred plus year old detente.
Enough of this stupidity, please. No matter how many times you regurgitate this nonsense, the smell is the same.