Although I agree with you, it's worth noting that this sentiment is not a new one. There were plenty of people who believed that WWI marked the end of war, at least in Europe.
Even after WWII, Pax Americana (in Western Europe) was not an inevitability. Today's relative stability in that part of the world was the result of enormous investments in intentional policy. As well as a fair bit of luck.
> Military might today is usually directed from superpowers to third-world countries, but that's a topic for another day
This sentence is a bit of a tautology [1]. But in any case, it's worth remembering that those incursions always find their way back home. Consider the most recent wars. The European migrant crisis has its roots in the most recent wars in Iraq and Afghanistan. Furthermore, the USA will eventually feel the economic impact of those two wars. The fact that [2] could happen while the USA ran up enormous deficits (completely unrelated to that growth) is deeply worrying; what will happen in even a slightly less dynamic domestic economy?
> China's influence and dominance will happen through the private sector, ironically.
This view of the world also has a time-honored tradition. Thomas Jefferson was an early proponent of the view that national power flows from economic might rather than hard power. It's worth noting that the policies he actually implemented while in office diverged substantially from his ideological beliefs.
I agree with you about what the future of conflict between the US and China will most likely look like. I think most people do. The question is how you hedge that bet: is the alternative military&economic peace (because military conflict is unimaginable)? Or, is the alternative military conflict on top of the existing economic conflict?
I think the latter is more likely.
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[1] https://en.wikipedia.org/wiki/Third_World
[2] http://ritholtz.com/wp-content/uploads/2016/09/virtually-768...