I think Hannibal's a special exception. I'm not sure which hannibal you are talking about, but they weren't they all engaged in a generations-long blood feud that lasted 300 years? I mean, this was not some simple faction conflict. It was a war between two rival states to decide the fate of the entire known world.
> weren't they all engaged in a generations-long blood feud that lasted 300 years?
I'm not sure how "exceptional" a multi-generational war was in medieval or ancient times.
There were Five Crusades between ~1100 and ~1300 for example. The Chinese Warring States period was 475 BCE to 221 BCE. Japanese Sengoku period (A similar "Warring states" era) was 1467 - 1600. The Hundred Years' War was 1337 to 1453.
There were times of peace, and then there were times of conflict. Sometimes conflicts that last centuries.
As a state vs state thing, Carthage and Rome definitely weren't unique in ancient times. Hell, Carthage wasn't even the last state that Rome engaged with in multi-generational war, they just came the closest to actually winning.
What is interesting about that particular war though is that it did span the literal generations of the Barca family, of which Hannibal was a member, and for whom at least two full generations that I know of all became leading generals in the Carthaginian army.
Rome is also somewhat unique in that they were basically in a state of perpetual war after a certain point in their history. War begat war, especially as the territory grew and the results of victory were wealth and prestige for the families involved.