Direct tornado damage is covered by private insurance. Damage from flooding (which will often accompany a large storm) is not.

https://www.allstate.com/tr/home-insurance/insurance-for-tor...

Subsidized insurance can maybe still make sense, if it is taking on the role of a deep pocketed reinsurer. Still, it should at least be structured to discourage people from living in the most flood prone areas, and carefully monitored to make sure it is administered as intended (inaccurate maps lead to incorrect rates).