Well, yes, at least compared to the Chinese. There are obviously a lot more Chinese than Japanese in the world, and in the US there are more than twice as many Chinese-Americans as there are Japanese-Americans. So if we assume that a roughly equal percentage of Chinese and Japanese people are going to become good actors, we’ll still have a much larger number of good Chinese actors both worldwide and in Hollywood.
But more to the point, regardless of how good they might be, there are precious few internationally known Japanese actresses. No cite, but I remember this as being the explanation given by the filmmakers for why the three biggest female roles went to ethnic Chinese actresses. There are no Japanese actresses as well-known to Westerners as Michelle Yeoh, Zhang Ziyi, and Gong Li, so if the studio was concerned with star power then they were kinda stuck.
At the time Geisha was released I remember trying to think of Japanese/Japanese-American actresses who’d be at all recognizable to American audiences, and I couldn’t come up with many. There’s Keiko Agena, best known as Rory’s Korean friend Lane on The Gilmore Girls, but her background is mostly playing supporting roles on television so she was unlikely to land a lead role in a major Hollywood film. There’s Youki Kudoh, the female lead in the film adaptation of Snow Falling on Cedars, but she actually is in Geisha in the role of Pumpkin. Otherwise the only likely candidate would be Koyuki (The Last Samurai), who IIRC doesn’t speak English.
That said, I also find the idea of geisha with Chinese accents rather silly, like having Scarlett O’Hara played by an actress with a distinct German accent. And seeing as how there were three big female roles, the studio might have taken a chance on a talented but not super famous Japanese actress for at least ONE of them. I haven’t seen any of her movies so I don’t know how she’d be in the role, but Rinko Kikuchi is about the same age as Zhang Ziyi and presumably could have played Sayuri. She was unknown in the US at the time of Geisha, but just a year later she appeared in Babel and received an Academy Award nomination.