We have flood insurance, but have never made a claim. We're not required to carry it, but being two or three feet above the flood plain in coastal Florida, there's no way we were going to decide against it. The bonus is that because we're not in the flood plain, it's cheap.
Honestly, from what I know about it, most of the problems stem from it being a program that has to coordinate with private homeowner's insurance with each of them only being liable some of the time. It's like when you have trouble with your phone, and the company that owns the infrastructure says it's the service provider's issue, and the service provider says it's a problem with the wires.
The claims issues have little or nothing to do with it being a federal program - look at Medicare, for comparison.
(And plenty of private mortgage lenders *do* require flood insurance when you're in the flood plain - just as they require termite certification - I'm as surprised as you are, that yours didn't.)
Speed comes from what you put behind you. - Judi Ketteler