Black characters are added regularly to movies in order to increase their inclusiveness. The dilemma faced by screenwriters is that Asian markets won't see a film with a black lead unless that black lead is Will Smith. So the black person won't be the hero, won't be the love interest. You can't change the villain to a black person unless they're extremely well written and even then someone's going to whinge so your villain is almost never black either. This means your black person is either going to be the sage that guides your protagonist through their hero's journey ("Red" in Shawshank - really, 90% of all Morgan Freeman roles) or it's going to be the token buddy who dies halfway through Act II. Movies are driven by economics, and the economics of movies are driven by foreign markets. This is particularly true of horror/slasher and scifi films. It's not that everyone in Hollywood is racist and sexist, it's that when you're making white movies for China, India and south Asia, they want to see white men being tough and white women being sexy (but not too sexy) and they have no interest whatsoever in your peculiar American obsession with Africans.
When you say "Asia", are you using the American version of the term, which is basically the Pacific Rim countries and China? Or the European "Asia" which includes India? My question really is whether Bollywood is as "black-averse" as the Pacific Asian market is...
India has its own problem with race: for example The issue of Indian actors and actresses being photoshopped so their skin tone appears lighter in magazines/on covers, etc, is a significant one in India/Bollywood, or that's my understanding, at least.
India is largely an indigenous market. You're generally safe assuming that the Pacific Rim will watch whatever the Chinese like. Bollywood produces plenty of content for India; the stuff they buy from the US is generally things that are big and expensive and full of explosions.