> I think there are examples both ways. Hiroshima, Cuban Missile Crisis, Berlin Crisis, involved escalations that were not met with further escalation.
Sure, nothing is 100%, but to address the parent point in detail:
First, there's a logical inevitability to that statement. If escalation never stopped, then the tiniest diplomatic insult would eventually result in nuclear war. If the diplomats do their job and the politicians listen, issues are deescalated whenever possible. It'd definitely possible to do. The point is that each escalation tends to increase danger for both sides; due to second-order effects, it's bad for the escalator.
Second, I think escalation does sometimes work when the escalator has such superior power that their enemy can't hope to match it. In the mid-1990s, China threatened Taiwan with missile launches. The U.S. sailed a couple aircraft carrier battle groups through the Taiwan Strait, a massive show of force that China couldn't hope to match at the time (they were militarily much less capable than now), and China backed down. On the other hand, China didn't back down: China felt humiliated and that event instigated the current decades-long military buildup in China, with a primary focus on the prevention of US aircraft carriers from intervening in Taiwan and naval control of nearby seas. Now the situation is more dangerous than ever, for Taiwan, China, and the US.
Finally, I don't think the examples in the parent support the case (though I'm sure there are examples that do).
Hiroshima: This event was during total war, when maximum escalation already had happened years before. Both sides were throwing everything they had at each other; one side happened to have more. (Also, the Japanese didn't surrender after Hiroshima.)
Cuban Missile Crisis: A prime example of the dangers of escalation; humanity almost was destroyed by nuclear weapons due to the brinkmanship of both sides. The USSR put nuclear weapons in Cuba, a clear escalation, and the US implemented a blockade to stop it; (both?) sides threatened war. It ended in a secret deal where the USSR removed its missiles from Cuba and the U.S. secretly removed theirs from Turkey. But I think the definition of escalation is tricky here: Putting the missiles in Cuba was an escalation, and the results matched the theory in the GP: It increased danger for both sides and achieved nothing. I'm not sure the US blockade was an escalation or a non-escalating response; e.g., an obvious escalation would have been for the US to put twice as many nuclear missiles on the USSR border as the USSR put in Cuba, and IMHO it's likely that such a (hypothetical) escalation would have again increased danger with no benefit.
Berlin Air Lift: That's an example of the opposite, a non-escalating response. When the USSR blockaded Berlin (a West German city surrounded by East German territory, other than a channel to W. Germany), the US (or was it NATO?) didn't respond by attacking the blockade or by blockading USSR cities; they simply flew in supplies around the clock until the blockade ended. They accomplished the goal without increasing the threat to the USSR.
I think there are examples both ways. Hiroshima, Cuban Missile Crisis, Berlin Crisis, involved escalations that were not met with further escalation.