Achilles was given two choices by his mother, either stay and die with imperishable fame or leave the war and live a life of peace. When he heard Hector killed Patroclus, to escape his fate and take revenge couldn't Achilles just leave that war and comeback for Hector at another time? And if he could, did he not see that because he was blinded by rage?
Achilles doesn't actually want to escape his fate. Turning away from the war at its outset is a response to Agamemnon's insult over Briseis. (The Iliad actually begins with this feud, and the major tension is over whether Achilles will ultimately participate in the war.)
The reason Achilles seeks his own destruction is that, in his case, his death is the price of undying glory. Undying glory he did achieve, as his name is almost as famous today as it was in Ancient Greece.
Consider Diomedes, regarded as second only to Achilles in martial prowess, with a case can be made that Diomedes actually exceeds Achilles in that Diomedes wounds two Olympian gods in battle in a single day. Yet I rarely hear people speak of Diomedes, who returned from Troy and founded numerous Italian cities.
As a referent, the Irish hero Cúchulainn was presented with a similar proposition: a long life in obscurity, or an dying young as the price of immortal fame:
When [Cúchulainn] was older, and near the time when he might assume the weapons of manhood, it chanced one day that he passed close by where Cathbad the Druid was teaching to certain of his pupils the art of divination and augury. One of them asked of Cathbad for what kind of enterprise that same day might be favourable, and Cathbad, having worked a spell of divination, said : "The youth who should take up arms on this day would become of all men in Erin most famous for great deeds, yet will his life be short and fleeting." Cuchulain passed on as though he marked it not, and he came before the king. "What wilt thou ?" asked Conor. "To take the arms of manhood," said Cuchulain.
SOURCE: Tales of the Ultonian Cycle "Cuchulain Assumes Arms" | See Also: Mythology: The Voyage of the Hero, p 48.
At a very basic level, acceptance of this bargain is a validation of the hero's courage, their willingness to die, and part of what makes them worthy of everlasting fame.
See also the Hagakure and Book of Five Rings. The Japanese concept of Bushido is quite useful in analyzing warrior heroes in that warrior societies, including Mycenaean Greece, tend to be honor/shame cultures.
This quote from the author of the Hagakure, Yamamoto Tsunetomo, elucidates the idea of the warrior's own death as a goal:
The Way of the Warrior is found in death. When it comes to either/or, there is only the quick choice of death. It is not particularly difficult. Be determined and advance. To say that dying without reaching one's aim is to die a dog's death is the frivolous way of sophisticates. When pressed with the choice of life or death, it is not necessary to gain one's aim.
Hagakure, Chapter 1