For what do you need to know the number of full moves? You still can't recreate every move in the game with FEN anyways, so I don't see the point of the full move counter. Is there any rule that depends on it?
You may want to record a fragment of a real game starting from move number 24, for example. Then you specify the FEN after the first 23 moves and set the full move number to 24.
One rule that depends on the move count is the time control. If you have a time control of 40/120, you need to know which move it is to know when the players get more time.