That's likely not because of government inefficiencies, but because a small segment of the population is responsible for the vast majority of costs. Mostly drunk drivers, to be frank - but also that certain lovely category of individual who feels that societal rules don't apply to them.
Private insurers can say "fuck no, we're not insuring you, you've got 2 DUIs, 6 speeding tickets, and numerous equipment violations" or make the cost of that insurance absurdly expensive, pricing them out.
If the government is providing the insurance, they likely have to say "yes" to everyone. Waiving the requirement to insure everyone is well and good until someone looks at the data and sees that your completely non-discriminatory rules are effectively discriminating against certain classes of people.
Private insurers can say "fuck no, we're not insuring you, you've got 2 DUIs, 6 speeding tickets, and numerous equipment violations" or make the cost of that insurance absurdly expensive, pricing them out.
If the government is providing the insurance, they likely have to say "yes" to everyone. Waiving the requirement to insure everyone is well and good until someone looks at the data and sees that your completely non-discriminatory rules are effectively discriminating against certain classes of people.