First and foremost upper body mobility is key in determining exactly where you CAN place your hands for the grip, but a big benefit to choking your hands as close as possible to the body is the contribution to full body tightness it allows. The next time you are setting up, with an unloaded bar place it on your back high bar position - start with a wide hand placement then slide them as close as you can to your body. Most people I work with immediately feel a difference in their upper back tightness.
To clarify, the upper body tightness is extremely helpful in maintaining a complete upright posture when you're performing the lift. Some forward lean is typical (normal), but as much as possible you want to maintain an upright posture with the bar being maintained over your center of gravity. (It makes sense, just think; the further forward you lean, the further ahead of your center of gravity the line of pull of the weight will be - placing a much greater strain on the low back to keep you from faceplanting. This leads to the classic squat-good morning that we always see).
Hope that helps out a bit!