China may have been militarily incompetent during these times, but wouldn't civil unrest eventually destroy the puppet governments Japan planned on establishing? What was the Empire's long game?
There was a faction in Japan who genuinely believed in the future vision of the "Greater Eastern Asia coprosperity sphere."
They actively tried to promote this idea among the intellectuals and academic elites of China and Korea.
Part of this was that they also convinced the Japanese ruling military factions that like Japan, the intellectuals of China and Korea would fall in line with Japanese military rule.
But the notion was completely impractical. Japan had no experiences dealing with the vastly diverse populations of China and Japan. Undoubtedly, some Korean and Chinese groups were sympathetic to the idea of a Japan led union type nation. But Japan failed to understand Chinese population would always feel foreign asserted overlords as no more permanent than the Mongols.
Japan's long game was to remove all Western influences in Eastern Asia, consolidate Japan centered alliances in Asia, and then contest Russia's hold on all of Eurasia.
With sufficient development of Asian resources, Japan would emerge as the dominant power in Asia, and then in the world.