The insurance industry has not traditionally advocated for mandatory auto insurance policies. They have traditionally favored selling their customers "uninsured/underinsured motorist policies" which you buy to protect you from the other guy who is at fault and is unable either through insufficent insurance coverage, or none, (because he is a deadbeat) to be able to pay your loss.
One reason is that they have already underwritten you and know your track record and can accurately underwrite their loss probability with you for that coverage. Another is they don't want to be forced to take those who are too financially irresponsible to purchase liability coverage to pay for the damages caused by their own negligence.
Several years back Texas was being pushed to allow illegal aliens to obtain drivers licenses. One of the main reasons given was that it would allow them to get to and from work so they could 'contribute to society'. In order to do so they had to be able to get insurance, minimum limits. Some insurance companies took a low profile and some just said they would follow the law. I argued against it for the above reasons and because it would 'normalize' illegal aliens and would be a first step to them getting Drivers Licenses in Texas. Next step was to get voting ability. The effort was not passed in either chamber of the legislature. I was just one small voice crying in the wind but a lot more were also crying out and the opposition was successful.
@ultrarunner, isn't it true that some pats of Cali now have illegals voting in some local elections and wasn't the Elections official for San Francisco an illegal alien? Didn't the state also mandate insurance availability for illegals and Cali Drivers Licenses?
Back then those who objected to DL's and insurance for illegal aliens were ridiculed as prejudiced and harsh. They knew then that they were pushing toward voter eligibility for illegals. What you have wound up with is a lack of avaolability of insurance coverage for your taxpayers. It still remains tbd if illegals will wind up getting to vote.