No, they did not, but not for the reason you suggest.

It's always possible to give some examples of individual warriors who were famed for their exploits in hand-to-hand combat. But these exploits never live up to the standards of Hollywood movies. In most cases these "heroes" are said to have defeated just a few opponents. Part of the reason Miyamoto Musashi Yagyu Munenori was credited with absolutely legendary battle prowess was the fact that he once killed 7 men in a single engagement. This is a far cry from the carnage of most pre-gunpowder battle scenes in movies and TV series; for the heroes of the silver screen, 7 kills is a slow day in the tavern.

However, the reason for the difference isn't that the chaos of battle would kill anyone well before they could rack up a notable list of victories. The notion that battle is a maelstrom of intermingled fighters is itself a completely fictional Hollywood trope. Organised warfare was a matter of formations: all your friends on one side, all the enemy on the other. The role of the warrior in such a formation was to hold his place, not to try and kill as many enemies as he could. Disorder was a greater enemy than the enemy. Encounters between infantry formations were not chaotic but tentative and probing; only in certain circumstances would mass be pressed against mass, and even then there would be limited opportunity for single warriors to kill very many of the enemy.

In other words, on most pre-modern battlefields there just wasn't any room for "great warriors" of the Hollywood mould. In the heat of battle, the number of casualties would be relatively low. Most men in most battles would never kill anyone, and would be happy enough just to survive. In any case, the great majority of them would be stationed behind the first rank with no means of reaching the enemy even if they wanted to. In such battles, most of the casualties would come when one side broke and ran, and the other chased the fleeing troops to stab them in the back with impunity. But there was little skill involved in that bloody process, and no movie is likely to celebrate the act of murdering the defenceless.

But then why do we keep telling those stories? Why do TV shows, books and movies depict battle in this totally unrealistic way?

One thing is certain: it's not just about a modern thirst for visual spectacle. Stories about great warriors scything their way through hordes of enemies are as old as time. Homer's Iliad, one of the oldest surviving Greek texts, spends several chapters on the aristeia (Great Deeds) of individual warriors like Diomedes, Patroklos and Akhilleus. For these heroes, simply killing droves of human warriors isn't enough; with the help of Athena, Diomedes defeats both Aphrodite and Ares when they appear on the battlefield, and Akhilleus famously takes on the river Skamandros.

But when we turn to historical sources, there are no parallels. The aristeia of real Greek warriors during the Persian Wars speak only of men who won a single duel, or who simply fought in a memorable way, without anyone apparently caring how many they killed. Finally the tradition of awarding aristeia seems to disappear. We also find both Spartans and Athenians actively punishing people for leaving their place in the battle line to go and take some heads. As I said above, organised warfare just doesn't leave much room for men to play the hero.

But how do you inspire warriors to give everything they have for their commander and community, if you can't show them some great examples? Just standing in a line and not running away is hard enough for men who have never been in combat. Most men would not want to do anything more than that. But it won't be enough to win. You need men to be willing to go and stab a guy in the face, even if he's trying to stab them in turn. So what do you do?

The common answer given by Greek commanders was to show them how it was done. Alexander the Great is the finest (or most batshit insane) example of this method: in every one of his battles, he flung himself into combat with reckless abandon, inspiring his men to follow him. We never hear how many men Alexander personally killed, and it really doesn't matter. Even in one of his most memorable acts of recklessness, when he was the first to leap down from the wall into an enemy fortress, he killed just one man before another incapacitated him and his bodyguards had to come to his rescue. But the point is that they did. They were willing to fight because their leader was willing to fight; they were ready to die because they saw that their leader was ready to die. It was his ability to inspire others that allowed Alexander to win so many fights.

The reason for Hollywood to focus on the sheer lethality of its heroes, even at the expense of all realism, shows that this particular form of leadership still has some of its old magic. But we should not mistake those depictions for historical truth, any more than we should believe that Diomedes defeated the god of war in single combat.