I don't think that's true historically, though it's more true in modern times. Basically with hereditary monarchies and such, you get what you get in terms of succession. For every Commodus there's a Marcus Aurelius. For every Vlad Dracula there's an Alfred the Great. But, succession wars tended to happen not when someone simply had a claim to the throne (as CK2 would have you believe

) but when someone had a claim
and was generally less likely to be a tyrant. People don't like being ruled by tyrants, so when a claimant needs the support of nobles or whoever else in a war for the throne, they'll only back him if he's not a tyrant. This was most apparent in England, though it happened elsewhere too. The more arbitrary and immoral a regime becomes, the more it sows the seeds of its own destruction. This was as true for the French Ancien Regime as it was for the Han Dynasty.
Now, as power became more centralized, this trend became less important and based on self-interest. Even still, the age of truly immoral rulers saw its heyday with the abusive colonial monarchies of the 18th and (more so) 19th Century followed by the ideological autocracies of the 20th Century. Democracies still tend to care about moral character, though there are obviously exceptions, these exceptions tend to be the kind that prove the rule.
Of course, it all depends on how you define "immoral." If you import modern "morality" (more cultural fashion, but that's another discussion) onto past figures, a lot of them will be "immoral." So I'm looking at it in the context of the time, adherence to the law, if any law existed (so executions aren't immoral if conducted properly, for example), general care for the welfare of the people, attention to higher principles as opposed to purely material gain, honor (including keeping true to one's word, treatment of foes, that sort of thing), etc. I'm not using any one particular moral framework since that wouldn't make any sense.