I think that Alexander had two audiences when he burnt Persepolis: the Greek and the Persian. To the Greeks, and particularly to the perennially troublesome Athenians, he was broadcasting his role as the avenger of the Acropolis, the man who had given the shade of Xerxes payback; but much more significantly, to the Persians, he was broadcasting the fact that their empire was dead, and the royal family with it. The fact that he later expressed regret for what he did suggests that he realised this policy had not worked – that the Persian nobility had been offended rather than broken by the act of sacrilege. And to the Persians, of course, the palace would not have been Xerxes’ specifically (‘the palace of Xerxes’ is, after all, a modern name for it), but more generally representative of Achaemenid royalty.