It's to keep college kids out. Four college kids can create quite a ruckus. We have the same ban in our neighborhood. We had three college kids in one house plus guests. They thought the mountain road was the Monte Carlo until one of them crashed into a tree. After they moved out, we had no more "racing" problems. The problem is that you sometimes catch others in the web. Our standard policy is that no one knows anything until a problem arises. We don't enforce unless there is a problem.
We have one college kid now. She was keeping multiple guests over until we threatened to call the homeowner that was renting to her. It was her parents.