Even though Family Feud is refered to as "The Feud" (as in "Let's play the Feud!") it wouldn't work as the official title. "Family Feud" is a common expression (before it became a game show).
Sure, it COULD work if they teamed up two teams of players that all had one thing in common (a la Hot Potato and Vs.), but the idea behind families playing was to see if family members think alike. Also, the idea of entire families playing a game show was a new idea at the time. They did actually consider doing a men vs. women show, but scrapped that idea... although a couple years later the concept was used in The Better Sex.