Unfortunately, I can only give a tangential answer, but it should explain the likelihood of such an event.

It comes down to battlefield psychology, specifically the fact that human beings, in general, do not like killing each other. I have seen statistics (although I cannot recall where from) that up to 90% of modern soldiers, with their powerful and accurate assault rifles, will either not pull the trigger at all or aim high with an enemy in their sights. Even if it could risk their own lives.

This is not a new concept by any means. Back when muskets were all the rage, soldiers were drilled to stand shoulder to shoulder, and officers would have a staff designed to knock all the muskets into a level line towards the enemy. They were drilled to be so close together so that it would be difficult to subtly move toward the back of the group or escape, although large blocks of troops are notoriously vulnerable to musket volleys and cannon shots. But the military leaders of the day understood this risk, and still believed it more important to keep people close together for the morale boost, and the ability to ensure that each inaccurate shot actually has a chance to hit somebody. (Pretty sure I remember this for John Keegan, The Face of Battle) And bayonet charges, if the attackers could maintain their momentum and reach a demoralized foe, more often than not broke the enemy on contact. If.

When the weapons are swords and spears, it was just as difficult (if not more) to get your soldiers into melee combat. There are entire societies who fight (or fought) primarily with missile weapons (see John Keegan, A History of Warfare). For example, Shaka Zulu was raised in an area where combat was fought on a small scale with thrown spears. Then he handed each of his soldiers and ilkwa spear, a broad bladed nasty looking thing that was only good for stabbing. But the surrounding tribes were completely unprepared for shock combat, and he was able to dominate the region. It is entirely possible, for instance, that Shaka took down many men in one combat, but it is just as likely that his veterans would be able to have done so as well. It isn't so much a difference of skill, as it is a question of willpower (and/or psychopathy). That one man in ten who will lead a charge, and is unafraid to get bloody, is terrifying and deadly to the average warrior. In Rome, these were the men who ended up as centurions, if they survived for long. In the world wars, they killed or captured dozens of enemies and got medals of honor, because they were willing to shoot when others weren't. Case in point, Audie Murphy, who actually portrayed himself in a movie after the war, but his exploits had to be toned down to appear realistic.

Of course, movies are heavily dramatized/choreographed, and have a time limit. Can I see one man kill twenty or more men over the course of a battle? Sure! Twenty men in the space of two minutes, however, is entirely unrealistic, unless they are running down a fleeing foe from horseback.

Sources that describe Alexander the Great all agree that he did fight in the front ranks of his men, beginning with the cavalry charges he led for his father Philip II's wars in Greece, and continuing throughout his campaigns in the east. At several points in the sources Alexander is described as being the first person over the walls of a city his army is attacking, and his men have to rush forward to prevent him from surrounded and killed.

These sources are all written down several generations (or more) after Alexander's death (though they are working off of several eyewitness accounts that are now lost), and there's definitely some mythologizing happening. But they generally agree that Alexander considered himself to be the heir of Homeric herosim (Plutarch says he slept with a copy of the Iliad under his pillow), and Alexander's desperate cavalry charges and willineness to be the first person over the walls are very much in keeping with the exploits of Achilles that he was trying to immitate. How true these stories were is difficult to prove, but it's pretty clear that Alexander did work to foster a perception of himself as the new Achilles, and part of that package was his willingness to put himself in the most important and dangerous parts of the battlefield.

This is probably not the most common approach in ancient warfare, however. Alexander was able to make it work because he had many trusted generals who managed different parts of the army while Alexander was leading the cavalry; this allowed him to set things in motion and then join the fight, rather than staying back to continue to direct the conflict. Plutarch deliberately contrasts this with Julius Caesar's approach to leading an army, which was to stay out of the front lines in order to direct the strategy (Caesar only gets his hands dirty when things fall apart and he has to stop his men from breaking and running away). Plutarch doesn't judge him for leading from the rear; he treats it as an accepted way to lead.

The scenes in 300 where Leonidas is cutting through Persians like a hot knife through butter are pretty much straight out of the Iliad. It's not how Leonidas would have fought (he'd have stayed in the tight phalanx formation), but it is the kind of combat that Alexander strove to bring to life in himself and his closest companions.

Richard III was, for all his misbegotten, Shakespearean reputation as some kind of vile cripple, actually something of a badass on the battlefield. His last charge against Henry (the future) VII being demonstrative - he had a battleaxe, and he knew how to use it.

Source: Richard The Third by Paul Murray Kendall.