The times described by the Iliad were remarkably different from those of classical Greece. There were kings, who looked for kleos. The decisive fighting was done by them, maybe because they were best armed, maybe because they were commanders that led by example.

Around the time of the fall of Troy (let's say 1200 BC), this world disappears. Thukydides ascribes this to the fact that these kings had spent too many years abroad, which allowed powerful factions to form at home. When they came back, they were killed or ousted, or had to fight hard to regain their place.

Even after the fall of the Mycenaean civilization, however, the cult of heroes keeps going. Many people claim to descend from heroes, like the Heraclides. The cities worship their ancient heroes in a way akin to gods. Sometimes, a man receives heroic cult after his death: the founders of colonies, for example, become heroes for their new cities. But this already shows a huge shift in mentality. The old heroes are great for their individual kleos, but these new heroes are great because of their relationship with their cities.

This shift in general informs the whole of classical Greece. The difference between free citizen and slave of a king was very strongly felt. Sparta had kings, but their powers were limited by the law. And the great legislators are never kings (Drakon, Solon, Cleisthenes, Lykurgos). The citizen body is what matters.

This also leads to a conflict between family code of conduct and city laws. We see it in Athens with the juridical handling of "honour killings", and in the theatre with the Eumenides and the Antigone.

Athens also imposes laws that aim to equalise the looks, size, and richness of tombs. Athens was unusual in its democracy, but it's interesting to note that the heroon, where the hero was worshipped, generally started out as his tomb. So it becomes impossible for families to start out their own hero cult of a fallen family member without the city's consent.

Anyway, a full citizen was supposed to feel first and foremost a part of his citizenry. By serving the interests of the citizenry, he served his own.