> what about empires that actually survived or adapted?
Really the Roman Empire did very well on this one, depending on when you date its final end to. But the pattern is there, especially if you look at the more rapid and more recent collapse of the Chinese empire, with the result of the Imperial line extinct and the successor state stuck on a relatively small island.
All administration exists on a spectrum from bureaucracy to personal intervention. You can break out Max Weber here, but it is generally agreed that a state needs a bureaucracy to be effective on a large scale. This machine "works" when it is functioning uniformly and according to process in order to achieve goals, and it breaks down when it is disrupted by a system of personal grift, favor, corruption and favouritism.
So the collapse of China runs roughly: poor leader (dowager Empress Cixi) -> ineffective state -> pushed over by foreign powers (European states vs Boxer rebellion) -> even worse leader (Puyi, last Emperor of China, took the throne at age 2) -> pushed over by foreign powers again (Japan) -> internal collapse of remaining China (Maoist rebellion).
Edit: forgot the Taiping Heavenly Kingdom rebellion, which belongs on the front of that list at about 1850, which is yet another civil war that killed somewhere between a quarter and a third of the population of China!
It would be a fun alternative history to swap the Japanese and Chinese leadership of the 1850-1950 era, such that Japan remains a feudal agricultural state and China got the Meiji restoration. How many carriers do they arrive at Pearl Harbor with?
> we all agree on the problem. What are all the solutions and how do we know they're the correct ones?
That is not at all how the last few years have worked, because an astonishing amount of lying about everything from basic facts to obvious outcomes is polluting the discourse.