On what basis do I assume the premium would be low if every firearm had to be insured? The cost would be a lot lower than it might be now, where insurance isn’t mandatory.
How would this insurance stop even one shooting, restore one dead person to life, or undo the damage done by criminals and why should law abiding people have to pay for it? You are advocating penalizing those who have done no wrong for the criminal actions of those who have. Unlike drivers who have "accidents" pretty frequently, few gun owners do. There are two separate groups involved: those with criminal intent who do the vast majority of damage with firearms and who will not comply anyway, and those who observe the law and are careful not to injure others (something that is far easier than it seems by simply following a few common sense rules).
Treat all firearms as loaded, at all times.
Check/clear/open the action of every firearm you are handed or pick up and make sure it is not loaded. Still observe the other rules.
Never point the muzzle in the direction of anything you do not wish to shoot.
Keep your finger off the trigger until ready to shoot.
Be aware of what is in the background, behind your target.
While firearms safeties are a wonderful additional device to prevent discharging a firearm without intent, never trust them to keep a firearm from being discharged. Only following the above rules will prevent injury.
These rules were ingrained in us at an early age, and habit by the time we hunted, which for most of us was before our tenth birthday.