Leaving aside Pax Americana to look at more settled history: none of those events were peaceful in global terms. There's a reason the general term is
pax imeperia.
The Pax Romana was 200 years of relative quiet after 700 years of effectively constant war, and followed by another 200 years of war. The thing most historians stress is just how far from peaceful it was. In practice, Roman-held lands were at peace because all resisting inhabitants were already dead, and peace on the border constituted a period of slowed conquest and retrenchment. As soon as the political situation deteriorated, both domestic fighting and foreign glory-seeking resumed.
The Pax Mongolica followed what was per capita the single bloodiest war of conquest in human history, wiping out perhaps 10% of Earth's total population and killing literally every person in several nations. The conquest stopped basically thanks a succession crisis. In return? About 200 years of relative peace and good administration, before the black plague fragmented the khanate. (And if we want to get cynical? The improvements to trade and travel under super- and hyper-powers are a key vector for pandemics. It's not sheer coincidence that disease ended the khanate.)
The Pax Britannica... well, it was accomplished mostly with vicious oppression and butchering local populations until resistance stopped. In return, we got about a century of quiet empire, ending in a global war and yet another world-shaking pandemic (this time, the Spanish Flu).
The history of imperial peaces is one of temporary quietude after an empire has killed off the opposition and reached a pause in its wars of conquest. Fighting remains on the edges, and the peace usually ends in yet another bloodbath as suppressed violence is unleashed - and often as disease wipes out large portions of the empire. It's peace by comparison, not absolute quality.
(The one thing to be said for the Pax Americana is that it's been comparatively bloodless. Even across a double-dozen shadow wars and conquests, the act of conquest was vastly gentler than its predecessors - but the history of such things does not inspire hope.)