It is all about game fairness. If your player loses, it should be his own fault. How many times have you died in a game(not stealth type either) simply because you couldn't react to an enemy or obstacle quick enough? Did it feel fair to you?
For example, you will notice in faster moving games, if they did it right, the camera could actually show more ahead than behind, simply so you have more time to see what is coming as you move. Since you are moving faster in that direction, most likely what is behind isn't near as important since you are likely outpacing it, while what is ahead is much more important. If you slow down or stop, than the camera should recenter you considering that what is behind has more chance to catch up, and because you no longer as far of a view distance ahead since you are slower or stopped at this point. Note that the above applies as well in top-view as it does in side-view.