Most likely there just wasn't a lot of Akkadian (Cuneiform) "writing" to be found outside of Mesopotamia, and particularly not what one would consider "literature".
Cuneiform was a logographic (1 glyph per word) system, that over time acquired syllabary (1 glyph per syllable) characteristics. Logographic languages, while pretty, can be very difficult to learn since they require a symbol for every word in the language. That makes popular "literature" more difficult to generate for them, and less rewarding, as only the very highly trained could generate or understand your novel. However, by the time the Akkadians got hold of it, it was more like a syllabary with some common pictographs kept. That's much more feasible.
The other issue Cunieform has is that its designed for use on clay or stone. A good size novel or even short story written in that medium obviously isn't very portable. A paperback of the Epic of Gilgamesh online appears to be about 128 pages. That much writing in fired clay tablets would probably weigh in the tons. Moving even a single copy would require an entire train of wagons. So you wouldn't expect to often find it very far from where it was generated.
So where would Akkadians have been generating their writings? Well, here's a map of the Akkadian Empire, and as you see its pretty much limited to the Tigris and Ehuphrates valleys, although they did do some campaigning towards Lebanon and Elam (SW Persia).
To be fair, they were the dominant power in the Near East at the time, so it would have been a common second language. However, literature isn't usually generated for an intended audience of largely second-language readers. They'd typically want to use their own language for that.
Of course by the Hellenistic Era, even better Alphabetic (1 symbol per vowel or consonant) systems has been developed and in use for nearly a thousand years. So anybody wanting to translate something like the Epic of Gilgamesh would have to go to where all copies of it existed, which would be somewhere in the area above. Since that's where all copies were, that's necessarily where nearly all Akkadian Cuneiform experts were too. (Can't learn a system you can't see).