Well, they did just that with the characters of Jack Crawford and Freddy/Freddie Lounds in the TV series Hannibal, by having Laurence Fishburne pull off a rather convincing and excellent Crawford, and Freddie Lounds is now no longer an oafish greasy fat guy, but a nosy woman journalist.
I'd say it works like a charm.
Would I personally accept it if Dr. Hannibal Lecter or Will Graham was suddenly black or latino? No, I don't think I'd like that very much. Just as I don't like Lucy Liu doing an ersatz Watson in 'Elementary'. Sometimes it works, sometimes it doesn't.
With movies and TV series, and movies and TV series based on books, there is a certain leeway you get by identifying and sticking to what really matters.
With iconic characters like those hailing from the comic book world, I don't think it's a very good idea. I personally don't like it. And that's not a racist stance, it's just a stance that strives to respect the source material. When you change something significantly, you're either adding payload that detracts from the original story, or you are creating an alternate universe from the position of a statement that could very well be interpreted as being revisionist.
We live in a sorry age in which we, on one hand, really seem hellbent on making everybody happy and creating equality, not noticing how unbalanced and off kilter everything has gone just in the last, say, twenty years. Characters and actors of colour are attacked pretty much instantly and described as being racist. Any depiction of a character of colour seems to get flagged for uncompromising scrutiny, making it a well trouble-laden thing, no matter the story or context of the character in question. Adding non-white characters can cause a ruckus. Having only white characters causes a ruckus. Turning white characters into non-white characters causes a ruckus. Turning non-white characters into white characters causes Gawker-level internet outrage. So... 'race' is obviously still a hot topic, and the only egalitarian thing I currently sense is that labelling everything 'racism' doesn't really help the situation, the people or the discussion much. Besides, it is evident that white 'racism' gets the shotgun treatment while any other-coloured racism seems to be getting ignored or labelled as a justifiable and totally logical thing. I take offense at that.