Have you read "The Fates of Nations" by Paul Colinvaux? It's a fascinating - and disturbing - book, covering the exact topic you are talking about.
But where Colinvaux and myself would disagree with you, is the direction of the cause and effect.
My interpretation is that a society starts off warlike. At some point it either conquers, or is conquered by its neighbors. Once the empire is at its natural borders, war no longer provides a good economic rate of return. People avoid the army and instead go into trade or farming. The imperial peace provides a stable base for commerce and industry. People become rich. As they grow rich, and as the need for martial valor declines, people become more decadent. They spend more on luxuries, they have less need for children. Thus both a decline in fertility and a decline in aggressiveness are symptoms of the underlying cause (war no longer being necessary for survival, and war no longer providing a good rate of return). Eventually though, on the borders of the empire some new, highly fertile, highly aggressive population arises. Meanwhile the old growth civilization has long lost its martial prowess, and each individual resident faces a game theory optimum of continuing the decadence, rather than face the rigors of a martial life. Thus the bordering tribe eventually is strong enough to invade, the old civilization falls, and the cycles of history continue.
According to Robert Wright in his book Non-Zero, future generations of both the conquering bordering tribe and the conquered old civilization (at least, those who survive) will derive benefits from the resulting cross-fertilization of cultures. That, he says, drives the combined civilization further up evolution's escalator. An example that comes to mind is England after the Norman Conquest.
I would dare to hypothesize that America history of immigration and cultural cross pollination could be a framework for a somewhat peaceful means of reaching the same ends.
But where Colinvaux and myself would disagree with you, is the direction of the cause and effect.
My interpretation is that a society starts off warlike. At some point it either conquers, or is conquered by its neighbors. Once the empire is at its natural borders, war no longer provides a good economic rate of return. People avoid the army and instead go into trade or farming. The imperial peace provides a stable base for commerce and industry. People become rich. As they grow rich, and as the need for martial valor declines, people become more decadent. They spend more on luxuries, they have less need for children. Thus both a decline in fertility and a decline in aggressiveness are symptoms of the underlying cause (war no longer being necessary for survival, and war no longer providing a good rate of return). Eventually though, on the borders of the empire some new, highly fertile, highly aggressive population arises. Meanwhile the old growth civilization has long lost its martial prowess, and each individual resident faces a game theory optimum of continuing the decadence, rather than face the rigors of a martial life. Thus the bordering tribe eventually is strong enough to invade, the old civilization falls, and the cycles of history continue.