Iggy -- it just looks better and it's more flattering. By framing somebody so their entire head is in a closeup, their chin ends up being too low to the bottom of the frame, their eyes too far down, and it's not as powerful.
In a wider shot, offsetting them a bit to the thirds of the frame as opposed to halfway in just provides a better composition. Your eyes have a natural rectangular field of vision, not a square or round one. That is, you can see more off to the sides than you can above and below in your periphery. Therefore, it's more pleasing to see images that sit from side to side (this is why film aspect ratios are wider than they are tall -- "widescreen") than ones that are narrow and make you read it from top to bottom.
EDIT: Here's a good example from "Kill Bill," shot by one of the best DPs in the biz, Bob Richardson (he also shot A Few Good Men, JFK, and Snow Falling On Cedars)/
And from a Chinese action flick:
You just want the strongest subjects of the frame in those intersecting points.