I would expect if you have liability insurance theres a lessened chance you would flee the scene of an accident you caused.

Every state I've lived in requires auto insurance.

The idea makes sense -- the state recognizes that vehicle accidents will happen and preemptively deals with free loaders by requiring auto insurance, instead of just suggesting it. It falls down when the state isn't actually requiring the insurers to do their damn job.

Mandating insurance makes sense from the perspective of CYA, though I wonder if the govt could do something to enforce competition. Maybe make public actuarist data, and payout rates and information?

Regulations frequently kill competition, either explicitly on purpose, or accidentally. Insurance is otherwise a hyper-competitive business anyway. Super easy to shop rates among many companies, so they all gravitate downward to about the same level, net of small differences in coverage or services, fancy websites, etc.

And of course uninsured motorist coverage is a thing, because making something illegal doesn't mean people won't do it.

If people engage in a risky activity where the legal system expects them to pay for damages if something goes wrong, but damage sums are so high that most people are unable to pay for these damages, it makes perfect sense to require people to have insurance if they want to engage in this risky activity.

The real crime is the state then zoning and building infrastructure in a way that forces you to engage in said activity, effectively forcing all citizens to buy insurance.