Why would people from a republic teach democracy to a republic?
Because by 23 BC the Republic was a republic only in name?
By this point Augustus had done the following (in American terms): made himself the permanent President and Commander-in-Chief - no more elections, disbanded the House of Representatives, converted the Senate into a rubber stamp agency, made himself the Supreme Court, declared himself the permanent head of the State Religion (actually declared himself a god, outside Italy).
And after 50 years of almost continuous civil war fought all over the empire, the vast majority of Romans and their subjects were very happy he had done so.