I *think* they are used for extra control! I've never used one before but I have put a rope over an EXTREMELY strong 14hh cob to stop him yanking me over!
Mazzie had one - in polo it's more of an Argentine design.
However if she put her head up high her standing martingale would come into play and she would feel it more with the rope noseband than with a cavesson as the rope was narrower = more pressure.
Mazzie (looking like a seaside donkey) with her polo bridle on.