> I wonder if Carthage had beaten Rome, the Phoenicians would take away the "ancient Mediterranean genius" slot away from the Greeks, since the availability of historical materials would be reversed.

I don't think we owe the survival of Greek sources to the Romans exclusively. Had Rome been destroyed and wiped out, we wouldn't have Latin texts, but the Hellenistic kingdoms could have carried on and Greek would have remained a prestige language in the Eastern Mediterranean.