We already do this to an extent. It’s called FEMA.
I am not against the government growing it’s role in this sector, I just would be concerned about the perverse incentives and subsidizing the very wealthy. Why should I have to pay for your nice house on the river that exceeds 8x or more my annual gross income? You couldn’t get private insurance because everyone knew this was a really bad place for a McMansion so you went to the government and got a free lunch. Also you are pretty much asking renters, who are usually poorer, to give money to homeowners who are usually richer.
Maybe if it was structured more like FDIC. The government provides insurance but there is a cap on how much. If you want more go to the free market.