The Enuma eliš is one of the later compositions in Mesopotamian literature, yes. The precise date remains uncertain, but it was probably composed in the Kassite period (Late Bronze Age, or the latter half of the second millennium BCE). Babylon had a long history extending back into the middle of the third millennium BCE (the Old Akkadian and Ur III periods), but it rose to prominence in the second millennium during the reign of Hammurabi, who seized control of most of Mesopotamia and reduced Elamite influence in the region.

First, keep in mind that the standardization of myths is a modern idea, and the notion that there was one "correct" version of a mythological tale would have been foreign to the people of the ancient Mediterranean. For example, Euripides and Herodotus claim that Helen spent the entirety of the Trojan War in Egypt, whereas the Iliad never gives any indication that the Helen in Troy was an imposter or a phantom. Several contradictory creation myths are attested in ancient Egypt, including the Ogdoad worshiped at Hermopolis (four pairs of male and female primordial deities, depicted as snakes and frogs), the Ennead at Heliopolis (several generations of gods, beginning with the god Atum and ending with the married siblings Osiris and Isis and Seth and Nepthys), and the Memphite theology attested on the Shabaka stone, a rather intricate creation myth that assigns the creation of the world to Ptah, the god of artisans.

Also note that literacy was very limited in ancient Mesopotamia. Scholars have traditionally underestimated the number of literate individuals in Mesopotamia, and Dominique Charpin convincingly argues in Reading and Writing in Babylon that kings, bureaucrats, high military officials, etc. were almost certainly literate to varying degrees. Still, relatively few people were literate, most likely a mere 1% of the population. The vast majority of Babylonians were not permitted access to the cuneiform archives of palaces and temples, nor would they have been able to read the tablets even if they had been allowed access.

When studying a piece of ancient literature such as the Enuma eliš, one should consider its function (its Sitz im Leben, as historians say). In this particular case, the creation myth was written as a text to be recited during the Akitu festival, the Babylonian festival celebrating the new year. The Akitu festival celebrated the lordship of Marduk (later called Bel, "lord") in Babylon and his close relationship with the king. At one point in the festival, the king prostrates himself before the statue of the god and is struck by a priest to symbolize his humility before the god.

When he (the king) reaches the presence of the god Bel, the šešgallu-priest shall leave (the sanctuary) and take away the scepter, the circle, and the sword from the king. He shall bring them before the god Bel and place them on a chair. He shall leave (the sanctuary) and strike the king's cheek. He shall place the... behind him. He shall accompany him (the king) into the presence of the god Bel; he shall drag (him by) the ears and make him bow down to the ground. The king shall speak the following once: "I did not sin, lord of the countries. I was not neglectful of the requirements of your godship. I did not destroy Babylon; I did not command its overthrow. I did not... the temple Esagil; I did not forget its rites. I did not rain blows on the cheek of a subordinate. I did not humiliate them. I watched out for Babylon; I did not smash its walls..."

The rituals of the Akitu festival were intended to reinforce not only the role of Marduk as the chief of the Babylonian pantheon, but, more importantly, the rightness of kingship and the divinely ordained role of his mortal representative, the king of Babylonia. In the Enuma eliš, the gods surrendered some their autonomy in accepting the kingship of Marduk, their newly appointed protector.

They set out for him a princely dais,

He took his place before his fathers for sovereignty.

"You are the most important among the great gods,

Your destiny is unrivaled, your command is supreme.

O Marduk, you are the most important among the great gods,

Your destiny is unrivaled, your command is supreme!

Henceforth your command cannot be changed,

To raise high, to bring low, this shall be your power.

Your command shall be steadfast, your word shall not be misleading.

Not one of the gods shall go beyond the limits you set.

Support is wanted for the gods' sanctuaries,

Wherever their shrines shall be, your own shall be established.

O Marduk, you are our champion,

We bestow upon you kingship of all and everything.

Take your place in the assembly, your word shall be supreme.

May your weapon never strike wide but dispatch your foes.

O Lord, spare his life who trusts in you,

But the god who has taken up evil, snuff out his life!"

Some scholars have read this as a divine parallel to the evolution of kingship in Babylonia from (proto-)democratic assemblies, which never fully disappeared at the local level, an interpretation first advanced by Thorkild Jacobsen in "Primitive Democracy in Ancient Mesopotamia" (Journal of Near Eastern Studies Vol. 2: 159-172). These assemblies have been studied more recently by Andrea Seri in Local Power in Old Babylonian Mesopotamia.

The pageantry of the Akitu festival would have made a deep impression on participants, who witnessed the majesty of Marduk and his mortal representative. The splendid dress of the king and his entourage, the parade of priests, other religious officials, and the emblems of the gods, the music and dancing that formed part of the entertainment during the festival, and the distribution of food and drink for public feasting marked the event as unusual and highly significant. That the Assyrians adapted the creation epic for their own purposes - substituting the national god Aššur for Marduk - suggests it was quite effective as a piece of political theater.

For more on the Akitu festival, see The Akitu Festival: Religious Continuity and Royal Legitimation in Mesopotamia by Julye Bidmead, Ritual, Performance, and Politics in the Ancient Near East by Lauren Ristvet, and Ritual Dynamic Structure by Roy Gane.