My hope is, just as it's commonplace for Chinese people to learn English, it becomes commonplace for Westerners to learn Mandarin. Only once we can communicate can we start to break through cultural and ideological barriers. It would be impossible to stop the flood of readily consumable Western Mandarin media and culture.
Unfortunately I think too many would see learning Mandarin as China winning a culture war, instead of seeing it as building a foundation for expropriating the CCP's control over Chinese ideology.
I definitely think there should be more cultural exchange, but as to your "missionary" plan of attack, it doesn't really work like that. If you really want to alter China having this fantasy that you're simply better than they are all you need is for them to see it will not help.
Many Chinese people already speak English, have lived and travelled overseas, but "dangerous" Western ideas have not penetrated into and changed their culture. The reason is not because: "the CPC controls it", it's because people Chinese people are very proud of who they are, and they accept the CPC is doing the right thing. Not meaning 100% agreement with the government -- it regularly bends to the will of the people to cool their anger when it's done something that didn't work.
Somewhat related to your point: I think people should definitely engage with China more, rather than just the biased hologram of China presented in Western media. That's good for everyone, whatever your goal is.
The culture bias goes both ways, and there's probably people who hope Westerners don't get a clear idea of China, and don't want them to learn Mandarin and engage more, because they're afraid of "Chinese ideas" penetrating and "expropriating" (to use your term) their culture and control.
Unfortunately I think too many would see learning Mandarin as China winning a culture war, instead of seeing it as building a foundation for expropriating the CCP's control over Chinese ideology.