Flood insurance is a different program.

No actual company is stupid enough to put money that a floodplain won't flood. Instead the federal government uses tax money to basically back insurance so that when, surprise, your floodplain floods, the insurance companies aren't actually losing money.

Not for flood insurance. There's no profit in it. The National Flood Insurance Program is a federally-subsidized program that loses about a billion dollars a year.

https://www.cbo.gov/publication/53028

National Flood Insurance is run by the government, it's not the same as most property insurance.