There's a quick, one-word explanation for why the federal government started selling flood insurance: Betsy.
Hurricane Betsy, which struck the Gulf Coast in 1965, became known as billion-dollar Betsy. Homes were ruined. Water up to the roofs. People paddling around streets in boats. Massive damage.
This would be the time when you'd expect people to be pulling out their flood insurance policies. But flood insurance was hard to come by. You could get fire insurance, theft insurance, car insurance, life insurance. Not flood.