It's a self perpetuating cycle that is proven
(just one of many articles last time this happened) to increase in times of recession. More people are prone to commit insurance fraud and make exaggerated injury claims. This puts insurance premiums up.
Meaning people have less money and are more prone to make a claim when they probably shouldn't. etc etc etc.
Even during periods of growth (ie the opposite of recession) this happens. Is it fair? Not really, blame the people making claims when then shouldn't.
The cost are car insurance is just one of the many things I don't think about. The wifelet's car is cheap, mine isn't, is about as far as I think about it.
There was a petition for a nationalised insurance scheme some time ago.
It didn't take off, only getting 44 signatures (though that may have been poor publicity).
Insurance companies do not make profit from our premiums. They take that money, invest in other markets (like many other financial companies do) and it's the profit from investment that drives the insurance company forward.
If the government were to run car insurance they would need to pay for it somehow. Either by putting premiums up, up and up (not really a favourable option), increasing tax revenue (might also lead to disapproval), or use the premiums to invest in other markets, to make money in order to pay claims. You see where this is going? The government are not the best at making profit, and profit is needed. Insurance cannot run on a not for profit basis as claims (and staff, overheads etc) will always need to be paid. And whilst predicting outgoing payments is quite accurate it is never perfect due to the nature of insurance claims.