> I feel like government stepping in and being the insurer with a sufficiently large pool of risk to spread around lets them set a fair rate without the need to make a return or answer to shareholders.
Youre about 20-30 years late to the game, but arrive in time to see the conclusion does not match your assumption. See california for fire, florida for fstorm damage, and everywhere in the us for federal flood coverage. It doesnt work. CA FAIR has higher rates to account for increasing the coverage pool, but it doesnt look like premiums will cover the current or future loses. Which is the universal story when your policy attracts all the high risk/payout buyers. And FAIR, roughly, is setup to go recoup losses from all the _other_ insurance providers in the state. Even ones not insuring those policy holders _or that type of insurance_. Its just a layer of indirection to subsidize fire risk against all poly holders.
In all of those examples you have the for profit private insurance leaving the market because it's not profitable enough. When you take away excessive profits and allow the governmental pool to compete with for profit insurance, risk is leveled across the pool and consumers pay less. If the big private insurance companies can't be more efficient or have better risk models than the government, well they should stop trying to sell policies.