> the mission of representing Chinese culture transferred to Singapore or Taiwan

This is certainly an interesting view.

Who would do the transferring?

All governments regulate agents of foreign powers, and thus can shut down the Confucius Institutes. Whether the replacement is called the Lee Kuan Yew Institute or the Chiangmai Kai Shek Institute is immaterial. The Chinese certainly don’t allow foreign NGOs on their territory and would have no grounds to complain.