"Chinese leadership is reasonably competent and has the luxury of nearly-total control. "
That's the problem. That's -why- they cannot multitask.
China has ruthlessly, methodically, and thoroughly beaten the very -idea- of personal initiative out of its people.
So every single little decision has to slowly, painstakingly move up the chain of command so that those at the top can say "Yes, you are allowed to paint the bathroom white". They get around the supreme, unimaginable inflexibility of this by making puppet corporations, these are lead by some rare individuals with personal initiative who are able to handle things up their -own- painstaking ladder.
We have aerial maneuvers, planned ship conversions, visible troop training. All for Taiwan, all requiring that the people at the very top personally sign off on it. I get where you are coming from, but you don't seem to quite grasp the sheer inflexibility of the Chinese system. If it's under the command of the central government then their focus is on Taiwan, if it's under the command of a puppet corporation then the central command only really loosely gives it suggestions and it has to then translate down the ranks, and then every single element needs to be hashed out by the guy at the top which -delays-.