I think you picked the wrong movie to use as your example. The story isn't presented as historically Japanese reality. Many movie or tv adaptations of books can have changes to race or even gender. In many cases this is for financial reasons, as the majority of the US movie paying audience is young white males, but that's not to say that couldn't change. There are many fine actors of many races that can perform any role. But movie companies are in this to make money, it's a business, not a cultural remembrance. Now if it was a real historical figure it wouldn't work. I think this is less of, we need a white person in this role, as we want a big actor in this role. Again this is a US adaption, go to other countries, Japan and China and they find local actors to fill roles, historically filled by Anglo actors. The interesting thing about the US, is we are a very diverse country of inhabitants, unlike Japan, or China, which have a much higher Asian populace.
Examples, like the Last Airbender, they didn't even pick a huge actor to bank on. And that had a lot of history visually of being Asian themed and they tried it in the movie, with mostly white actors. Outside of the movie being awful, that backfired. But take Will Smith, playing Jim West in Wild Wild West (though again an awful movie), I suspect movie studios would be fine with Will Smith playing any character as he is bankable (mostly...). Or look at Irdis Elba potentially being the next James Bond.. I think that would be fantastic. And I don't think anyone would really care.
There are plenty of examples with changes in characters to try a different take on things. Let's re-do that plot but with female leads. Or let's take that plot and make it in space. Or let's take Dances with Wolves and make them Stupid Blue people who instead of offering beef jerky to animals, connect with the animals via (never mind it still is weird).
Point is, the US has a very low Asian population, and we've done a poor job or portraying Asians, in something other than Kung Fu or Doctor roles. Action movies, typically have a strong male lead, and someone like the Dwayne Johnson, Diesel, Smith, can perform those roles, just like Tatum, Jackman, or a Stallone could today. But I look forward to the day to seeing another top actor, say of Hispanic or Asian decent take command of the screen.