Maybe part of it is economic risk. Localization and distribution would have some costs, and maybe nobody's willing to take a risk on "let's bring China's #1 movie to the US". Things like anime in the west got bootstrapped in obscure fandoms on an informal, low-budget, and sometimes downright bootleg way, which I'm not sure they want to do if they're trying to consciously develop soft power.
I am somewhat surprised about how limited China's attempts at soft power seem to be. They don't have a prominent global media presence like, say, the BBC/DW/NHK. They don't seem to be tooting their horn well about their engineering advances. They don't even seem to have effective tourism marketing-- I can't think of the last time I saw an advertisement encouraging travel to China (even before the pandemic) while there are loads of travel documentaries on TV all conveniently sponsored by "(random state or European country) Tourism Office"
I do think a missing piece is having a few more world-beating brands. Yeah, we have a few, (Lenovo, for example), but we're definitely at the point where people will say "I'm not going to buy a Chinese car/washing machine!" -- which feels about where Korea was in 1980 or Japan in 1955.
Amazing how fast attitudes change. Just a few decades back, Japanese goods and Made in Japan had the same cheap, low quality reputation as Made in China goods today. I even distinctly remembered the same "Japanese people as a culture don't care about quality" comments which is the same as some people nowadays complaining that Chinese people have "chabuduo"(just enough) attitudes. Or the same accusations of no creativity.
Funny how drastically these "deep-rooted" cultural attitudes in Japanese people have changed. Or maybe its not the culture of Japan that has changed but the perceptions others have of it. I reckon the same is for China.
This said, we won't have a real tipping point until China can rival Hollywood for quality and quantity of cultural output, and their language makes that quite difficult. This is one of the reasons the USSR never "won" even at the time when it was arguably more powerful and efficient than the US.