[Jack Simth]

Narf:
Actually, you can, you just need a very large wad of cash to dedicate to it (at least, in the US). For instance, there's a particular amount of car insurance required (I don't remember the details, I'll call it $20,000 for now) to legally drive where I am. This is in case you get into an accident that's your fault - you have to be able to pay off the other guy to at least a minimum amount. If you can demonstrate you have the money squirreled away and dedicated to exactly that, that's your insurance - and it can draw interest (which you can siphon off). Theoretically, the law requiring the insurance is to protect everyone else (if you don't have the money, you can't pay their hospital bills) when you're at fault.
Some things are not required by law, but by contract. In this area, when you buy an actual new car, the contract on the car requires that you have full coverage until it's paid off - this is contractual, and is designed to make it so that the dealer doesn't lose money if you get into a wreck and see no need to continue payments (normally, if you simply stop paying, they can repossess the car; they can't do that effectively if the car is doing an accordion impression).

As to Insurance companies never paying out:
Don't know about your location, but in mine, they are actually legally obligated to pay out a particular minimum percentage every year - this still leaves them a big profit margin, but if nobody gets into a wreck, the car insurance company is (effectively) legally obligated to go smash headlights or something so that they can pay out on an insurance claim (fortunately, people in general are reckless enough that this doesn't happen). On a more personal note, my dad has been the beneficiary on an insurance company paying out an insurance claim - car insurance, specifically; got rear-ended, his insurance company got the money for the repairs from the other insurance company. All told, took maybe two or three weeks.