It's important for the Chinese government to have the trust of the Chinese people, but foreign opinions matter as well.
The US has sharpened its propaganda machine from decades of cold war with the Soviets and has the ability to topple governments they want with ease through channels like the CIA, "democracy activists" and propaganda news. Their tentacles are absolutely everywhere, from every issue imaginable like "3 gorges environmental activists" to youtube channels like RealLifeLore. It is extremely easy to fall for average westerners to fall for American propaganda.
All these have very real consequences. We've seen Europe starting to adopt a more hardline policy against China due to the "uighur genocide" fake news and the Hong Kong protests that were flamed by Mike Pompeo. We've seen racist attacks against asians all over the west.
All these will get worse if China's CCTV doesn't buck up and come up with proper counter-attacks.
How is that going to make a difference, the west already make up their mind It is driven by combination of fear, insecurity, racism, frustration from being abandonment by their own elite, helplessness, etc
No amount of messaging is going to change their mind . Case in point in Nazism in Germany in 30's I mean German are high culture people, with poet, humanist like Goethe and Schiller. Yet they fall of failed sergeant Hitler because he can express their frustration, fear and grievances better than those reasonable, noble critic.
I mean China try , they open CGTN America modeled after RTV and Aljazeera. They produced video explaining China position and show real China. They invite foreigner to produce video sympathetic to China cause and show real China
But did anybody listen NO !
So of course they should keep trying. But the ball is not on China court It is up to the western elite, politician, media, industry to make up their mind. Are they going to live in peace with China or not ? No amount of explaining or messaging is going to do if they can't make up their mind
What China can do is prepared for the worst and hope for the best!
Any reasonable person should know just by looking at history in the last 40 or 50 years how many war that the west get involve and how many war did China get involve?