On the insurance issue, requiring law-abiding folks who wish to own / carry firearms to buy it is a restriction that leaves too many things open for abuse. Once such restrictions are in place, it becomes much easier for a partisan politician to screw over the law-abiding folks.
For example, if you take a look at the City of New York, they crafted a bizarre, twisted network of laws that made it all but impossible for ordinary law-abiding citizens to own firearms (currently being whittled away by the DC v. Heller and MacDonald v Chicago rulings).
The crafters of such legislation assured the populace that such restrictions weren't going to affect the law-abiding, but in the end, look at how things were badly twisted. These days, the authorities there don't issue permits, even though courts have repeatedly ordered them to issue them.
As for accidents, you're trying to impose a law that only affects a minute amount of the population. If we look at the National Safety Council's 1998 statistics on deaths:
Heart disease 737,563
Cancer 538,455
Stroke (cerebrovascular disease) 157,991
Chronic obstructive pulmonary disease 102,899
Doctor's negligence 93,329
Motor-vehicle 43,363
Firearms (Total) 35,673
and out of that Firearms total...
Suicides 18,503
Homicides 15,551
and of course...
Accidents 1,125
1,125 accidental deaths is a paltry amount, when you look at basically screwing over the entire law-abiding populace. If you want to play numbers with other accidents...
Falls 13,986
Poison 8,461
Drowning 4,350
Fires, burns 3,761
and, of course...
Firearms 1,125
For those who claim to be neutral on the gun-grabbing argument, you'd see that 1,125 is a lot smaller than any of the above, yet why aren't you calling for buying liability insurance for insecticides, cleaning agents, and other toxins? You'd certainly have over 6 times the impact...
Or, why not making a swimming license and insurance? You'd save over 3 times as many in that case.
In the end, you'd give me the same answer I gave you, proving my point, that such mandates would have no real effect on the law-abiding populace, nor would it discourage criminal behavior.
Remember, we don't force people to eat healthier, to exercise more, to get regular checkups with their doctor, take EKG measurements, etc. If you're not going to force hundreds of millions of people to take such measures, even if it would help close to a million people (from the heart disease and pulmonary obstruction categories) to do so, why would you propose something that would have only affected 1,125 people?