Car insurance is one of the biggest scams perpetrated in America...no one cares about safety, its all about how local and state governments require it, and then they co-operate with companies to scam people by over-charging for the least rationale possible through "official" channels.
Actually... (boring post coming)
...Most car insurance companies don't make very much money from car insurance (if anything, even).
They make their money by investing their 'float' and earning returns on that. Basically, they take in x every month and pay out x the next month. For that month they can invest x in the market and earn a profit.
THAT's where their earnings come from. So there's really no scam here. They CAN'T make themselves much cheaper. Many insurance companies actually lose money on the insurance part of the business in an attempt to gain more customers.
So why are prices so high? Well this might sound familiar, but the problem is health care costs. Paying for injured people is a lot more expensive than fixing cars, and the costs for THAT has been going up and up and up for everyone. Car insurance companies included. THAT's where your GEICO check is going...to pay for someone's surgery; not their bumper.
In fact...I hadn't thought of this until just now...but is it a coincidence that the OP has low car insurance rates AND lives in a country where the government supplies health care? Hmm...probably not.
Now, clearly there's something to your theory about regulations. That's why it varies from state to state. NJ clearly requires things that are more expensive than other states. So I agree with you about the government requirement part raising prices. But that's a state-to-state comparison thing. Not a company-to-company thing. So as for the "they charge too much" part, that's clearly not the case. These companies want market-share above all else. Trust me, they'd lower their rates if they could. It's one of the rare industries where you can actually believe them when they say "we want to get you the best price possible." They make a bigger profit by having more customers giving them a bigger float...they're gonna do everything they can to get more.