After 39 years of study of Military History I am still concerned with a matter that bothered me back in 1971. There is a tendency in wargamers to bend the military reality to fit the rules (yes I have done it too!).
Lets take the square. Who came up with the idea that a square could not move? Reading at the moment includes Mark Adkin: The Waterloo Companion, and he follows the same line as Barbero in his Waterloo Book in saying the Guard Chasseurs attacked the Allied line in square. Adkin also makes a valid point (with diagrams) that this formation is no harder to maintain than a full line when proceeding in a nominated forward direction. Consider that some of Wellingtons Allied Officers memoirs mention their units moving forward in square and we have food for thought.
Finally, Before and after this period it was not unknown for British troops in India or Africa to move about in square