There’s an argument for maintaining a reserve

In a federalized system where you print your own currency, there's really not. Insurance premiums become a deliberate dampener on economic growth that offsets the possibility of future spending (and subsequent inflationary risk) during a large disaster, and an incentive to mitigate risk in order to reduce expenses.

But there's no money in simply holding cash in reserve. That's why private insurance companies typically try to parlay their premiums into investment ROI. The real money in running an insurance company is what you can do with all the cheap cash you've collected while you're sitting on it, with the expectation that you won't need to pay it all out again any time soon.

A public system wouldn't need to hold cash in reserve that it can print/loan itself at ZIRP. And it wouldn't need to seek private ROI ahead of inflation or to pay off private investors in order to mitigate the risk of holding large volumes of cash for a long period of time. But - most importantly - a public insurance program attached to a large state/federal government has a financial incentive to mitigate risk on travel that it can combine with actual public policy to improve the economy overall.

Rather than just insuring a house or a car, state officials can implement public works that reduce the risks of flooding, provide emergency relief during natural disasters to mitigate loss of life, and reduce instances of highway accidents / fatalities. Instead of simply outsourcing and privatizing the risk management aspect to an independent contractor, they can attack the problems of social risk holistically, then set policy prices to reflect the risk-adjusted negative externalities of cleaning up a mess created by risky individual behaviors.

Must be nice