This middle Kingdom phenomenon is a recent creation. Mao had not thought about it at that time. At that time it was simply teach Imperialist India a lesson and show the Chinese awaam that they are the good guys and the coward Indians are thieves. Mao had already destroyed Chinese culture you would think he would care for buddhism or Tibet. At that time their strategic reason made more sense to connect Xinjiang with Tibet and have a shorter road and travel time. That's now a jugular vein for their control of Tibet and Xinjiang. Cut that G219 and we can destabilize both of these provinces. It's like Malacca strait but for land. Maybe they are doing all this drama to increase the size of the buffer so that it takes longer for us to attack that highway. Anyway The present leadership wants to revive Chinese culture that's why there push for Chinese traditional medicine. So using buddhism to increase there territorial boundaries into Arunachal. Who knows...Sorry dude, that does not compute. Why? Had that been the reason, China would have taken over entire Ladakh in 1962 itself. That time India was really really really weak and China had massive fear of rebellion in Tibet. Also, there was no point of withdrawing from eastern theatre.
In present scenario, It will be impossible for China to actually support war effort in Ladakh to capture it. If war drags on till winter, they will either have to retreat or will be butchered badly.