The old reasons for overdraws are long gone. As mentioned, the idea was so you could shoot a shorter, lighter spined arrow to gain more speed. With the advent of thin walled aluminums and carbon arrows it's just not useful anymore.
As mentioned, because the rest is mounted behind the grip (pivot point) of the bow and movement is exaggerated so accuracy can be greatly affected.
Also, there are carbon arrows out today that weigh anywhere from 20gr/in down to about 6gr/in which allows an archer to shoot much lighter arrows at full length. Longer arrows are more stabile in flight so have the tendency to be more accurate.
Just make sure you don't choose too light of an arrow. The higher the poundage and longer the draw can produce much more stress on the limbs and other parts. The general rule is a minimum of 5gr/lb of bow weight. This can produce the highest speeds, but often you want a little more weight in a hunting arrow to make the bow more quiet. Something like 6gr/lb or even a little more can work well.