Although the law may differ by nation, generally insurance for using an object does not cover its illegal use - be it a car or a weapon.
It's very likely the insurance on a home and contents that includes a legally-owned gun might be null and void if the someone is shot with by accident with it, or if it is stolen; if the owner had failed to ensure its proper security.
Also I imagine a lot of insurance companies might be happy to include a sporting shotgun in your property, if they can sure the weapon is legally owned and securely protected; but might ask why you would want a military style gun. I dare say there are policies in the USA for such guns, probably through gun-clubs, but would it really come under normal house and contents cover, and would a criminal bother with insuring it anyway?
Insurance cover is normally for genuine accidents or certain events beyond the policy-holder's control; and would not cover anyone for holding illicit property or engaging in illegal acts.
Compulsory cover might help the authorities know who has what weapons where, and may help after an accidental shooting (fatal or not).
It may also assist in confiscating for destruction, weapons whose serial numbers have been erased, are dangerous even to their own users, or which have been modified without authority to make them more lethal; should those appear second-hand.
(A gun modified to ensure permanently it cannot be fired, probably an antique, is another matter; though threatening someone with it, or with even a never-working replica, may be itself an offence in some jurisdictions.)
+++
As an comparative aside to that, although I have never and will never own a gun; I am pretty sure that in UK law a legally-licenced, fully-working fire-arm kept at home must be stored unloaded in a locked cabinet of an approved design for security. I don't know how it and its use would be insured; probably through an accepted agricultural or sports-shooting organisation.
I read recently about a scale-model of a 19C, muzzle-loading, gunpowder-fueled heavy mortar. The originals were not infantry weapons but big things usually installed in coastal-defence batteries. The model was of course non-working, but if its builder had added details allowing it in theory to be fired, although using only a small projectile and of short range, it would have to be licenced.
