Chinese media isn't going to get more popular in other countries because they start catering to Western audiences. Chinese media companies simply aren't good at that and their efforts are just going to look pathetic. Just look at all the Hollywood productions that were aimed directly at Chinese audiences - they all missed their mark badly because they didn't know what they were doing.
It's better to simply continue doing what these are good at. Plenty of Chinese media has gained popularity in Southeast Asia and other places without having to compromise. Sure, a lot of it is because these places have a lot of Chinese diaspora, but if the quality wasn't there, then they wouldn't have gotten popular. My take is that if the quality is there, the material will be able to find new audiences. And if the quality isn't there then it doesn't deserve to.
Also, I'd note that Chinese media gaining popularity overseas doesn't have to mean popularity in the West specifically. Sure, this might be the ideal goal, but China faces a lot more obstacles to this than other countries do, and it's possibly more valuable to be successful in other regions. For example, China gaining soft power in Southeast Asia or the Middle East might be more meaningful than doing so in Europe.