There Were A Few Things Plato Didn’t Account For

The reason history repeats itself in collapses is that there is competition between the growth of a civilization and human nature. As a civilization grows, it builds infrastructure. With infrastructure comes COMPLEXITY and the inertia of all that has been built resisting needed change. Human brains, which have not evolved much since the Stone Age, can’t deal with it. So human psychology slips back into the primitive behaviors that the Stone Age brain evolved to survive. The culture wipes out its plentiful local natural resources during favorable weather conditions and collapses when the climate turns against them.

In the past, there were always new frontiers that provided abundant natural resources for new civilizations to sprout and keep humanity going. Things are different now. This is what Plato didn’t account for. To summarize a few of the key issues:

Resource Depletion: The reason the Roman Empire expanded as far as it did was resource depletion. Rome needed wood for war ships. Greece had depleted the great forests around the Mediterranean. Rome pushed all the way to Germany and England for wood and water. Humanity has now covered the globe. We are experiencing resource scarcity in minerals, soils, water and places to dump our waste products. This time, there are no more plentiful resources to bail us out.
There are too many people. There are more people alive today than all the humans that ever lived before the start of the industrial revolution. Given that those who lived took 8,000+ years to deplete most of Europe and China, we are facing the ability of those now alive doing the same thing in a few generations , but no longer having Europe and China to pillage. Plato surely didn’t anticipate this. And modern humans, and their institutions, relying on history as a model, are in complete denial about the time compression of modern technology and power tools.
Complexity: Both the goods and services modern society uses are so complex that even our best institutions can’t predict their interaction. As the resource depletions cause hardship and starvation, people will fall back on selfish primitive behaviors. But they will have at their disposal, modern capabilities, like machine guns, home made bombs, and mobile communicators that can coordinate their clan warfare across the globe.

None of this changes your model. It just speeds things up, makes the overshoots higher, the collapses deeper, and any possible recovery much harder.