>What makes you think "myth of Jesus the Christ turns out to be, say, a cipher of the re-execution of Alexandros I, the son of Herod the Great and Mariamne I" is at all likely?
It's not just Nicholas of Damascus that would reveal such information. Gaius Asinius Pollio, a multifaceted Roman figure known for his connections with literary giants like Virgil and Horace as well as Augustus himself, mentored Alexander, the son of Herod the Great. The Roman world in the first century was wide.
Anyway, as to why I think it's possible, I think it's the most simple explanation as to how it emerged. According to what we have (i.e. Josephus) Alexander had the support of the public but was disliked by Herod's loyalists due to his opposing qualities and lineage from the Hasmonean dynasty.
Herod the Great, notorious for his brutal tactics, killed off male members of the Hasmonean dynasty and married the last Hasmonean princess to solidify his rule. He exhibited suspicion towards his wife Mariamne who was also killed eventually, along with their son Alexander.
I posit that Alexander was not actually executed, being a popular favorite and the son of the tyrant who might regret his decision and punish accordingly. Instead, he laid low until Herod's death, aiming to rightfully claim the throne, but was instead executed to maintain Roman rule over Judea with the consent of the Sanhedrin.
After the First Roman-Jewish War, continued supporters of Alexander coded secret histories into what became the apocryphal and synoptic gospels. Episodes like the massacre of the innocents coming from the Hasmonean male purge, "Jesus" being found in His Father's temple coming from Alexander visiting the building site of the Second Temple erected by his father, Herod. There are plenty of other episodes that seem to neatly correspond to and dispel underlying "mysteries" in the synoptic gospels for anyone actually looking for them.
The survival of works by Asinius Pollio or Nicholas of Damascus in particular in the Herculaneum library could confirm or refute this theory. Their writings, likely popular in aristocratic households due to Nicholas and Gaius Asinius Pollio's favor with the Julians, would very much be pertinent to a Roman aristocrat in 79AD.
But I don't need to prove it via circumstantial and inferential evidence--that's why I'm excited. We could actually uncover period documentation by the actual participants rather than the heresay of the following generations living under the shadow of Roman retribution.