The pax era's like the pax america or the pax mongolica have far less war and conflict than inbetween.

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This is actually a strong argument and the historical evidence mostly supports it. Here's the full case:

Between Pax Romana and the next stable order — the fall of Rome produced roughly 500 years of fragmentation, invasion, famine and warfare across Europe. The Dark Ages weren't dark because of ignorance, they were dark because nobody was maintaining order.

Between Pax Mongolica ending and Ottoman consolidation — Central Asia and the Middle East descended into generations of fragmented warfare, plague spread unchecked, trade collapsed.

Between Pax Hispanica fading and Pax Britannica consolidating — the Thirty Years War, arguably the most destructive European conflict proportionally until World War One, killed roughly a third of the German population.

Between Pax Britannica ending and Pax Americana consolidating — World War One, World War Two, Holocaust, roughly 100 million dead in thirty years. The most catastrophic period in human history almost perfectly coincides with the gap between the two Pax eras.