I can't prove this, but consider that hand writing is pretty much the only thing that allows humans to provide extended reach to their accumulated learning, across generations and centuries.
Without hand writing, or something like it, to act as a physical artifact and provide shortcuts to skip over expensive processes of trial and error, I doubt that a codified language, borne of strictly oral traditions among small pods of disorganized dolphin social groups, would survive across generations, to jump the inheritance gaps introduced by being hunted nearly to endangered status by predators like us.
If they're as smart as their neurology suggests, maybe they could learn our codified languages, or one we can develop cooperatively and share, through careful training on both sides.