The Chinese entertainment industry has historically had a lot of restrictions and problems. There is no question that this has limited China's "entertainment power." For instance, if games did not have to be approved by the government - which could decide to freeze new games approval for a year if the higher up politicians decided they didn't like kids playing games - there would be more investment, creativity, and faster development. Tons more young people would be willing to join the industry, and international success would be significantly improved.
But is it worth it? Does China actually want to be an entertainment super power? Historically, I don't think it did - the CCP, like the Soviet government, saw art as a vehicle for propaganda, and not a commercial industry. Further, I don't think the older generation of Chinese government officials actually knew how to achieve it, even when they decided it was important.
Chinese animation is probably the best example. China was a pioneer in animation outside the West. Princess Iron Fan came out just four years after Disney's Snow White - the first feature length animated film in history - and two years before Japan's first animated feature length film. The film actually inspired Osamu Tezuka, considered the "father of Japanese comics" - to take up comics, and also inspired the Japanese government to create their first animated film.
But what happened to the Chinese animation industry, after? The answer is that it was turned into a propaganda factory during the early years of CCP rule, and subsequently, during market reforms, it was left behind because, being a government sponsored effort, that generation of Chinese animators never had to make a "product" and so were totally not prepared to compete against the mature industries of the West and Japan, which subsequently flooded China with their products, creating the well-known phenomenon today of generations of Chinese kids growing up with anime and Western cartoons and imitating it.
Later, the Chinese government tried to revive the Chinese animation industry by restricting foreign animation on Chinese TV and throwing money at domestic creators. This is a similar strategy to what China did to catch up in manufacturing, but it largely failed to produce results until the rise of internet media companies. Why? Because entertainment is not manufacturing. You can't compete on price in an industry where people's time is the most valuable, and where piracy is rampant. People would just choose to pirate anime instead of supporting "cheap domestic animation." Building up an entertainment industry means investing in quality and content worth watching.
Fortunately, the rise of media platform companies injected much needed expertise into the industry. A new generation of product managers and creative leads who knew the field much better than the government officials managed to do what they could not: execute a successful generation skip into 3D TV animation - where China is now the leader - while also establishing the necessary talent search, development, and collaboration programs with Japan to grow the industrial base in traditional 2D. Chinese animation is still not where it wants to be, but it's now a close third behind Japan and the US.
The general lesson, though, is to be careful of what you ask for. The Chinese government has traditionally not been a great supporter of popular entertainment, and even more importantly, they have historically not had the skill set to support it properly. Entertainment, more so than any other industry, requires private, market oriented leadership. The best policy for a government is to provide funding for talent development, and then step aside. Entertainment power will come with time, as wealth increases and people start pursuing higher satisfactions than their basic needs. We're already seeing it happen in China, today, as a richer population begins to elevate their tastes and wallets. The government just needs to not be an obstacle.