Caveat: I’m not a high-level fencer; I only tried out fencing for a while in college. On the other hand, I have been involved in martial arts for years, including instruction, and have a keen interest in all kinds of combat arts.
Three things occur to me:
When you see video, you’re not seeing things from the perspective of the opponent. Their torsos might be more rotated from that perspective than you think. In my first dojo I learned the trick of pointing a staff directly at an opponent’s eyes so that from their point of view all they see is the end, which makes it hard to judge the overall length of the staff. Someone looking from any other angle wouldn’t see that detail.
Assuming what you see in the videos is true, however, what you’re supposed to do isn’t always what you actually do. People under pressure revert to instinctual movement and early trained habits. This is why retraining a poor movement pattern takes so much more time than learning a new movement pattern from the start. Combat stress quite often impairs higher cognitive functions. This is particularly pronounced when there’s actual danger involved. Read The Secret History of the Sword by J. Christoph Amberger, and On Combat by Dave Grossman for more information on combative psychology and physiology.
Anecdotes of even highly-trained competitive fighters reverting to near-neophyte status under combat conditions are very common. Non-combat competition stress unquestionably has some impact on performance. Stress inoculation is not often included in competitive training, though its importance is recognized in most of the combatives community.
The classical foil fencing position was taught when competition swords were heavier — closer to the weight of a real rapier or smallsword — and only single-time movements were feasible. Now, with double-time movements with foils so light and whippy that you can literally score a touch on the center of the back by flicking your foil over your opponent’s shoulder, and rules governing right-of-way in attacks and the rigid enforcement of target areas without regard to feasiblity, the side-on position has less meaning. If you look at epee fencing, the stances and responses are closer to classical fencing due to the greater weight and rigidity of the blade.
Reaction time and distance control are far more important in the modern game for sabre and foil fencing. While that classical position is probably better in some ways for presenting a smaller target and promoting a slightly longer lunge, it’s not as good for rapid movement and recovery as a more square stance. Fleche or flying attacks have also become much more popular than they used to be, which means more square-on stances just because of basic biomechanics.
Sometimes you’ll see high-level fighters deliberately present targets to their opponents to provoke an attack in a predictable place. Experienced fighters will suspect a trap, but so much of the action in a fight between trained opponents takes place at a near-reflexive level that often one of them will take the presented target anyway, either out of instinct or gambling that their trained pattern of responses will beat the other at the end of the movement chain.
Pistol shooting positions used to be taught with a side-facing stance for the same reason as fencing. Historically, you’d practice shooting for dueling or combat, so you’d either want to present a smaller target to your duel opponent, or practice the same kind of stance you might use when fighting in close formation or with the pistol in an off-hand (until repeating firearms were invented, a pistol was only good as a backup; the primary weapon would have been a sword, rifle, or bayonet). That changed a lot as the technology of firearms evolved and battlefield tactics changed drastically due to those developments. Fencing, obviously, was more static since real combat with live blades has virtually never occurred in the past couple of centuries.
Now, the most widely taught pistol stance is usually some form of either the Weaver or isosceles stance. Fitting natural movement patterns better, solidly supporting the weapon with both hands, promoting rapid target acquisition in line with the sights, and bringing the weapon back on target after firing are all rightly seen as far more important than the very slight difference in target size you achieve from presenting only one side of your body to your opponent.