Seems to be historically wrong

At least the hype for the program is that Julius Caesar, by making himself dictator, ended the Roman Republic.

That's just not true.

Back in the 50s a chap named Sulla marched on Rome and made himself dictator. But after a few years he retired and the republic continued as before.

No, what ended the republic was 20+ years of civil war, first between Caesar and Pompey, then Brutus and Cassius against Octavius and Marcus Antonius and then Octavius vs. Marcus Antonius. After all that chaos and strife, the people were willing to go along with anything so long as it restored order.