Speaking generally, it makes sense, for LD$, inc. to encourage the parents to keep their missionary offspring on the familty policy. Here, in no particular order of importance, are some of the reasons why:
1. males between 16 & 23 are high risk. Most of you parents remember the horror you felt when your agent told you how much more per six months you were going to pay once Junior got his learners permit. So if LD$, inc can get you to pay for the missionary, that saves them quite a bit of money.
2. Maybe LD$, inc could get a 'global' (or at least a US national) policy, but the cost would be pretty high, because besides the obvious foreseeable administration hassles (adding new drivers, deleting existing drivers, getting underwriting reviews on the new drivers and rating them, as in, any kid with a ticket or chargeable accident will cost more than the clean record kids) the 'global' carrier would probably demand that LDS, inc self-insure a certain amount of the liability coverage, just like the normal deductible on first party coverages (Comp & Collision). I kid you not, it would cost a small fortune, on top of having to add people to LD$, inc's payroll.
3. Every time a missionary changed his location, there'd have to be an underwriting review. There'd be a huge variety of variables involving cars and each location needs it's own rating. Here in my area the working missionaries are on bikes, but there are areas, I'm told, where they'll have to drive a car.
But here's something that I know pertains to California, and it's probably not alone among the States: insurance follows the car. In CA, no registered owner can put a car on the road without liability coverage. So when Elder Missionary gets into a fender bender on the 101 freeway, the other driver, and the cops, want to see the insurance card for the vehicle. The cops are going to be a mite upset if the Missionary tries to tell them to use his personal insurance coverage; either the car has coverage, or it's gonna get impounded and the driver issued a citation for driving an uninsured vehicle.
So it stands to reason that cars being driven by California missionaries are covered by a policy purchased by LD$, inc; the permissive drivers of said vehicles are covered. In a serious loss, any insurance available to the individual missionary could be 'stacked' on top of the LD$, inc policy, but that would be like asking the Coca Cola truck driver to add his little $15/30 policy to the Coca Cola policy, which for all intents and purposes is limitless. I imagine a plaintiff attorney who found himself suing a missionary as the agent of LD$, inc would be drooling about how deep LD$, inc's pockets are.
Which brings up this issue: Where is your son serving his mission and did you specifically receive correspondence asking you to keep him on your policy? You could save some serious coin by deleting him from your policy for the rest of his mission. What's the worst that could happen, that he's always ridding shotgun?