So, Sinbad’s 3rd is a reimagining of book 9 of The Odyssey, but the question remains, why? Why not just rewrite Odysseus as the hero they need him to be? The first part of the answer is easy. They wanted their own hero, someone from their part of the world. Greek heroes are fine and good, but they only speak to Greek culture. Sinbad is a hero of the Arab world, representing that culture. It’s only natural that they would want to tell stories of their heroes instead of relating what the Greeks did.
This is not a new idea, either. The Romans readily assimilated Greek mythology with their conquest, making Heracles into Hercules and Odysseus into Ulysses, but they also had their own hero Aeneas who also copied and piggy-backed off of The Odyssey (at some point I may even go through the Aeneid).
Part of the reason for Sinbad is to give the Arab world their own cultural hero in the same vein of Odysseus. Many cultures feature some type of wandering heroes. Sinbad’s 3rd Voyage copies more closely than others, but it’s still valid to establish Sinbad as the hero of his culture.
The culture also dictated why it couldn’t be Odysseus, but more on that later.