Does the coach (in white) in the above picture look like he is going to move quickly? Is you were asked to move as quickly as possible in any direction, would you choose this stance as your starting point?
However, this position is not far from the instruction that I received as a player, and the instruction that I heard at basketball camps early in my coaching career. I was told repeatedly by very good coaches that this position will make a defender faster. It never seemed to work for me, as my coaches continually told me that I was slow. Only when I ignored their instruction, in summer leagues without my coaches or once I was done playing, did anyone refer to me as a competent defensive player, athletic, or quick.
As with most things, the specific defensive stance depends. It depends on the individual, and it depends on the situation. More on defensive stances in the videos below.
One of the most frequent instructions that I have seen, especially at camps, is the coach walking around and pushing players in their shoulder to check their balance. However, this is stability, not balance, and it is not even desired: