The notion that rival power centers bring peace is ridiculous. Your own example proves the contrary: Rome destroyed Carthage after years and years of war. The notion that the US wields some sort of Pax Americana hegemony over the world is equally wrong. Iran, Cuba and many other countries Rome would have wiped out continue to exist, albeit with sanctions. Yes, Iraq, but that is an exception that proves the rule.
In reality US wields influence over the world to prevent any global player from developing an empire of hard control, because such hard control is bad for stability and commerce.