Stories like the Iliad don't feature the exploits of heroic warriors just because they make a cool story. These legends focus on supernatural feats of martial prowess because they reflect a society in which bravery in combat is crucial to the social status of warrior elites. As the hero Sarpedon puts it to his comrade-in-arms:

"Glaukos, why in Lykia do we receive special honour as regards our place at the table? Why are the best portions served to us, and our cups kept brimming, and why do men look up to us as though we were gods? And we hold a large estate by the banks of the river Xanthos, fair with orchards and wheat-growing land; it becomes us, therefore, to take our stand in front of all the Lykians and bear the brunt of the fight, so that one may say to another, 'our lords in Lykia eat the fat of the land and drink the sweetest wine, but they are good men; they fight well and are ever at the front in battle.'"

-- Homer, Iliad 12.310-321

Other sources from the early Archaic period confirm this picture, in which one's status and value to the community was defined by one's willingness to "fight in front", take risks, and kill the enemy. Feats of strength and bravery would allow the warrior elite to justify their high standing: they lived up to their reputation and earned their wealth by proving themselves better fighters. Status flowed from good service in council and war. Rewards were given to those who distinguished themselves in combat. In this environment, it is not surprising to find stories built around the incredible exploits of supernatural heroes - a suitable mirror for all those who aspired to greatness. While we have no contemporary evidence of historical wars or warriors from this era, we can assume that there would have been some warriors who exceeded their peers in skill or audacity (no doubt in more modest and more attainable ways than the heroes of the Iliad), and were consequently praised and rewarded as heroes.

Even as states became more organised and the role of rich front-fighters gradually shrank, it remained useful to encourage the spirit of the heroic epic. In a world without professional armies, putting a high premium on valour was one of the most effective ways to ensure that the ordinary people who were forced to defend their community would do a decent job of it. They were supposed to think of themselves as potential heroes, who might win glory and renown by performing well in battle. These lines by the Spartan poet Tyrtaios express the values of the front-fighter in a general levy:

This is excellence, this is the noblest prize and the fairest prize in the world for a young man, this is a common good both for the city and all her people: when a man stands firm in the front without ceasing, and, making his heart and soul endure, banishes all thought of shameful flight, encouraging his neighbour with words. This is a man good in war; he quickly turns the savage hosts of the enemy, and stems the tide of battle with his will.

Over time, Greek heavy infantry levies solidified into regular formations on the battlefield, and individuals pushing to the front to distinguish themselves ahead of the mass of the army (the sort of behaviour praised by Homer and Tyrtaios) became less important than the actions of the mass as a whole. Nevertheless, the old values persisted. It is in Herodotos' account of the Persian Wars that we find the first historical evidence of the aristeia, a prize offered after a battle to the person deemed to have fought the best. This was a clear encouragement to all warriors to play the hero. Herodotos recounts the debates among the Greeks at Plataiai as to who merited the prize:

According to my judgment, the bravest man by far was Aristodemos, who had been reviled and dishonoured for being the only man of the three hundred that came alive from Thermopylai. Next after him in valour were Poseidonios, Philokyon, and Amompharetos.

Nevertheless, when there was a general discussion about who had borne himself most bravely, those Spartans who were there judged that Aristodemos, who plainly wished to die because of the reproach hanging over him and so rushed out and left the formation, had achieved great deeds, but that Poseidonios, who had no wish to die, proved himself a courageous fighter, and so in this way he was the better man.

These won the most renown of all who fought at Plataea. (...)

Of the Athenians, Sophanes son of Eutychides is said to have won renown, a man from the town of Dekeleia (...) From that town was Sophanes, who now was the best Athenian fighter in the battle, and about him two tales are told. According to the first, he bore an iron anchor attached to the belt of his cuirass with a chain of bronze. He would cast this anchor whenever he approached his enemies in an attack so that the enemy, as they left their ranks, might not be able to move him from his place. When they were put to flight, it was his plan that he would pull up his anchor and so pursue them. So runs this tale. The second which contradicts with the first and relates that he wore no iron anchor attached to his cuirass, but that his shield, which he constantly whirled round and never held still, had on it an anchor as a device.

-- Herodotos 9.71-74

Interestingly enough, this is not the first mention of Sophanes. This Athenian warrior had already distinguished himself in an earlier conflict against Aegina. When the Athenians gained the upper hand, the Argives sent a group of volunteers to reinforce the Aeginetans, but they proved insufficient to turn the tide:

Most of these never returned, meeting their death at the hands of the Athenians in Aegina. Eurybates himself, their commander, killed three men in single combat, but was slain by the fourth, Sophanes of Dekeleia.

-- Herodotos 6.92.3

The historian's focus on these heroic exploits has often been explained away as a mere desire to make his work more epic - in a literal and figurative sense. Since there was little in the way of a historical tradition for Herodotos to adhere to, he adopted conventions from different genres that suited the story he was telling. In his descriptions of battles, he clearly leaned to some extent on Homer - telling of great moments worthy of epic poetry like the fight over the body of Leonidas at Thermopylai. On the other hand, Hans van Wees has argued (in Greek Warfare: Myths and Realities (2004), 182-183) that we shouldn't dismiss his anecdotes of individual heroism too easily. Herodotos described a conflict that had occurred in living memory, and repeatedly tells us who had told him the stories he tells. It is most likely that the Herodotean fighting style, combining early hoplite formations with occasional old-fashioned heroics, accurately reflects a way of war transitioning from front-fighter individual heroism to more organised, collective fighting. In this window of time, there was still room for famous warriors, and Herodotos duly records their names.

But this was a dying world. Herodotos' own account already shows the conflict of values prompted by the new form of warfare: was Aristodemos more heroic for rushing forward in a berserk rage and getting himself killed? Or was true heroism displayed by Poseidonios, who held his place and saved his own skin and that of his neighbours in the line? The Spartans eventually settled on the latter. They began to recognise that a thirst for individual glory was detrimental to the integrity of the army. As such, it was no longer desirable to encourage men to be heroes. The aristeia occasionally recur in Greek sources, but it is not clear whether they continued to be a regular feature; it is likely that they were phased out except as a morale-boosting reward. Men with heroic tendencies were henceforth to submit their recklessness to the interests of the community. The last thing we hear about the Athenian hero Sophanes was that he was killed commanding an imperial expeditionary force:

Long after this, Sophanes met his death when he was general of the Athenians with Leagros, son of Glaukon. He was killed at Datos by the Edonians in a battle for the gold-mines.

-- Herodotos 9.75

There is, of course, no stopping elite male authors from admiring the prowess of exemplary warriors. Throughout Ancient literature, there are stray references to heroic deeds, like Iphikrates hauling an enemy across to his own ship while wounded, or Isidas the Spartan fighting the Thebans oiled up and naked, with nothing but a spear in his hand. After the reckless antics of Alexander the Great, personal martial prowess became a cornerstone of the status and public image of Hellenistic rulers. But the credit for victory increasingly went to commanders showing careful planning and shrewd tactics. From the fourth century BC onwards, statues and inscriptions commemorated the deeds of generals, not warriors. The shift in attitudes is perfectly expressed in this anecdote from Plutarch about two Athenian generals:

Timotheos was right, when Chares was once showing the Athenians some wounds he had received, and his shield pierced by a spear, to say, "But I, how greatly ashamed I was, at the siege of Samos, because a missile fell near me; I thought I was behaving more like an impetuous youth than like a general in command of so large a force."

-- Plutarch, Life of Pelopidas 2.3