I think the movie should have ended where we see her sad on the cliff.
The rest looks like an effort to give a happy ending.
I mean even the reason that she is later called looks unreasonable and suddenly all ends well.
Given the attention to detail the film has this looks almost intended, like an add-on sawed to the end.
It always felt that way in the book a little. Having read it a dozen times, however, I've grown slightly fond of it. The Chairman mentions that he kept his distance because he wanted Nobu to be happy, and if you flip back through the back, you can pick up on some of those moments. They did a better job of showing his conflicted feelings in the movie because...well, it's a movie; you can actually see him.
And IIRC, the book is a bit sadder and more ambivalent; we hear about the Chairman dying, Sayuri describes having to be kept somewhat isolated because of the Chairman's association with Nobu, etc. The final line describes memories washing away like watercolors, and it always struck me as being somewhat melancholy, as if from a woman who must admit her life was far from picture-perfect. But for me, the saddest part will always be not knowing what happened to the other geisha, and not knowing what made them the women they are. (Those would be great spin-off novels; one about Hatsumomo would be especially popular, I bet.)
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I would love to read about Hatsumomo's life. It would be interesting to find out if she was always unstable or if events in her life caused it. And I would like to know what really happened to her after expulsion from the okiya.
Most of the others probably wouldn't warrant an entire novel except maybe Mameha, but maybe a book with a chapter or two on each woman.