The now Italy region had a new leader every year for a stretch, until eventually Julius Caesar. We see as the video progresses, the mean leader reign per count

The now Italy region had a new leader every year for a stretch, until eventually Julius Caesar. We see as the video progresses, the mean leader reign per country/region seems to go up significantly. Like the bubbling cauldron is congealing. I don't think what you're observing there is plausibly described as an instance of some general law of increasing stability. What you're talking about is the transition from the Roman republic, with a(n unwritten) constitution that mandated annual elections, to the Roman empire, whose rulers (typically) remained in place until death.