Because private insurers have incentive to accurately price risks. If they price them too low, they will go bankrupt. If they price them too high, the competition will steal their customers with lower rates for the same coverage.
The governments, on the other hand, don’t go bankrupt, so when they price the risks too low, the public will be forced to bail it out anyway, either through taxes or through inflation.
This very much is real and serious problem: consider, for example, National Flood Insurance Program, which is exactly the kind of publicly controlled insurance you asked for. It was $25B in the red by August 2017, and would have gone bankrupt if it was private. However, you (and other taxpayers) bailed it out in October 2017 to the tune of $16B. It continues to accumulate debt, and is more than $20B in debt right now. You will bail it out again, and keep subsidizing people who build their houses on flood prone areas, knowing that you will pay for their losses.
It's no different from the GFC, where the risk (of those mortgages) are mis-priced, and in the end, someone is left holding the bag.
A functioning market to redistribute risk needs transparent pricing, and proper bankruptcy (so in other words, the risk taker must not be bailed out, even if it hurts in the short term).
The governments, on the other hand, don’t go bankrupt, so when they price the risks too low, the public will be forced to bail it out anyway, either through taxes or through inflation.
This very much is real and serious problem: consider, for example, National Flood Insurance Program, which is exactly the kind of publicly controlled insurance you asked for. It was $25B in the red by August 2017, and would have gone bankrupt if it was private. However, you (and other taxpayers) bailed it out in October 2017 to the tune of $16B. It continues to accumulate debt, and is more than $20B in debt right now. You will bail it out again, and keep subsidizing people who build their houses on flood prone areas, knowing that you will pay for their losses.