Interesting. Its is not required where I live (Kansas), but I know people who have voluntarily done it. Just for their own protection, some people don’t want to sell a gun to a complete stranger and have him turn around and do something terrible. If you go to websites that facilitate private sales, like ‘Midwest gun trader’, some of the ads will say “FFL Required”. Some of these are dealers, but others are individuals who are voluntarily doing the check.
Yes, as a seller if the weapon has any history you might want to go through the FFL.