chillindan
really, you would never make a right turn in a left hand pattern? ever?
so, let's say you were on base leg and encountered another plane head on? he had made a mistake and was making right traffic to the same runway you were making (correctly) left hand traffic.
you were head on, you wouldn't turn right under any circumstance? two planes head on should both turn right in my part of the world. (assuming all else was equal)
IF you turned left and he kept turning right wouldn't you end up pretty close?
Wombat and others: what do they solve? It gives you a keen awareness of the wind. Compensating for the wind to achieve a ground track that is desired. As in the case of a rectangular pattern associated with a traffic pattern. Not understanding the wind might make you overbank to hurry a turn, instead of planning ahead. Overbanking/steep turning in the traffic pattern might put you closer to a stall.
IF you are not aware of wind and you simply make 90 degree heading changes to make a traffic pattern, the wind will drift you away making a pattern that doesn't really look rectangular.
Circling an object on the ground allows for observation, simply maintaining a bank angle will cause you to drift away and not allow for observation of something on the ground (like a wind sock).
Some pilots never really understand how the ground speed changes over the course of a simple rectangular pattern. I can't imagine a pilot really having a feel for the plane and maneuvering in a prescribed fashion without practicing ground reference maneuvers.