There's still the matter of the storage media, though; as far as I know, cuneiform never "made the jump" from stone and clay to lighter, more portable materials like parchment or ceramic ostraca. If it were able to do that, then Aramaic would have very few concrete advantages over it indeed.
If Akkadian writing had made the jump to parchment, would we even know? Parchment is not exactly imperishable after all. I have heard it speculated by well-known Greekists, that almost all documents in Linear B would have been written on parchment (or perhaps papyrus), but that only writings on clay survived to the present. Ironically, the surviving texts were actually the least valuable ones, not considered to be worth the expense of writing them on parchment, but only on cheap and easily recyclable clay. The ones we have were all baked in the fires that caused the destruction of the buildings they were located in, they were not intended to be kept for more than a fairly short time.