The real problem was actually people with homes along the Mississippi River as it was well known to flood fairly regularly. But never the less people would rebuild their homes exactly as they were before every single time just for them to flood and be a total loss again. Eventually private insurance companies deemed flood an uninsurable risk and refused to cover it. This is in turn drove up the reliance on federal assistance for those affected by flooding.

(It's important to note that all states in the US have been affected by flooding, either cyclical or flash, at one time or another.)

Once it became virtually impossible for people to get flood insurance the US government, when it was reasonable, stepped up and created the NFIP under FEMA to provide flood insurance to the public. The NFIP is designed to be a sustainable, not necessarily profitable, insurance program on its own and as mapping and modeling for things like floods improves it's rating gets more in line with the risks it insures. That said it does get hamstrung by the government that created it by only allowing certain percentage amount rate changes for renewing customers and such but it is functioning like an actual proper insurance company.

Also, like all insurance the more people the NFIP insures the better off it is as it spreads it's risk over a larger number of risks. Sadly flood insurance isn't required everywhere so most of it's risk is concentrated in high risk flood areas which is why it has the coverage limitations it does.

But to get back to original point what you are actually bitching about is FEMA not the NFIP. FEMA comes in and helps people regardless of what insurance they have.

Edit: And Citizens Property Insurance in Florida as well since the population of Florida pays to prop it up when its losses get to big. So you could bitch about that as well. Or the lack of regulations to force people to retrofit and build more wind resistant structures. Lots to bitch about other than the NFIP.