So, the latest "easy answer" (to the U.S.'s gun promlem) that seems to be washing across the various social sites I visit is the idea of "require insurance for gun ownership and you'll make guns too expensive to carry!". On the face, it sounds good. I mean, car insurance isn't cheap for most people and medical insurance is stupidly expensive. So, why wouldn't gun insurance be expensive, too?
Problem is, the cost of insurance isn't high just as a matter of course. Insurance costs for many things can actually be extremely low. What drives insurance prices is generally how much it costs for an insurer to provide coverage to a risk-pool. This includes things like administrative costs, but the real drivers of costs are the annual payouts to be covered. Those payouts are driven by two main things: the costs of claims and the likelihoods of having to pay out those claims.
Car and medical insurance are both expensive - particularly medical - because the likelihood of having to pay a claim and the size of the claims are both high.
If you've ever been in even a fender bender and looked at just the cost of body-work, even trivial incidents can be stupid expensive. Throw in personal injury claims and then take the number of claimable incidents that happen over a given amount of time, and you come up with fairly high risk-exposure for an insurer.
Similarly, if you've ever been the customer of an ER for something minor and then looked at your EoB, you've noticed that even "small" emergencies are stupidly-expensive.
With both automobile and medical insurance, insurance rates are highly variable. Some peoples rates are punishingly-high while others' may border on trivial. Why? Actuarial tables and claim-history. Insurers look at your age, your health, your personal habits, where you live and other indicators of risk (likelihood of payouts and likely sizes of payouts). Those factors are evaluated and you're put into risk-pools of people with similar evaluations. The insurer then has to determine, "give a pool of size X with a likely annual payout of Y for that pool, how much do I need to charge each of that pool's members to be able to turn a profit". Insurers can further decide "do I make my profit by providing coverage to a small number of subscribers that I get fat margins on or do I make my profit by providing coverage for a larger number of subscribers but where each subscriber earns me a lower margin". In non-competitive markets, insurers tend towards the former. In competitive markets, the temptation to do the latter is higher (gain customers by undercutting your competition).
Thus, even if one were to pass legislation saying "gun owners must be insured" (and courts don't ultimately see such legislation as infringing on exercise of a constitutional right), it's entirely reasonable to assume that not all insurance will be prohibitively expensive. Indeed, if such mandated insurance were to prove prohibitively expensive, it would increase the likelihood of courts deeming an insurance mandate an infringement on exercise of a constitutional right. You have to figure that, unless there's artificial restraint of competition, there'll be at least one or two insurers that would do the math and figure out that they can make serious bank by providing low-margin/high-volume insurance policies.