Italy's collapse of long-standing city-state governments, combined with the unpredictable, non-hereditary turnover of the papacy, created a 'perfect storm' of instability that only a single power with hereditary staying power near Rome could stabilize.
Ada Palmer explains that Machiavelli wrote The Prince against a backdrop of two compounding instabilities: nearly every Italian city-state had recently had its government overthrown, and the papacy's unpredictable, non-hereditary succession meant an unfamiliar, often hostile ruler every decade or so.
transcript
Ada Palmer: When Machiavelli was born, there were six or seven city-states in Italy that had had their governments uprooted recently. By the time he’s writing The Prince, it’s dozens, in fact, the majority of these places. So it’s volatile. Almost no government has staying power.