On first read, as a child, I was charmed by this Newberry Award winner. Then I grew up, studied Chinese, and took the time to research children's books that can help introduce Chinese culture to American children. It turns out many or most of these stories aren't actually folk tales, but original stories by the author in the folk style. Meanwhile, the author's background knowledge for creating "Chinese" stories didnt include experiences in China. I realized that although some of these are good stories, many aren't the least bit Chinese, and they can be very misleading. Chinese children aren't likely to be drinking milk, for example.
Folk tales (and imitation folk tales) that introduce superficial trappings of a foreign place are available from many sources, but I'd recommend that you hold out for folk tales that allow the reader a window on a different way of life, particularly a different set of values or priorities. In picture books you might like Bautiful Warrior by McCully, Zen Shorts by Muth, Everyone Knows What a Dragon Looks Like by Jay Williams, The Nightengale by Hans Christian Anderson (or some adapted verison of it), or Round is a Mooncake by Thong. In chapter books you might like Young Fu of the Upper Yangtze by Lewis (also a Newberry Award winner), Daughter of the Mountains by Rankin, or veer of to Korea for A Single Shard (also a Newberry Award winner).
No clue how this book remains in demand. First of all, the stories are rather dull, and the names are so similar as to be very confusing. More importantly, though, these are not authentic Chinese stories. Rather they are written "in the Chinese style" by an American who never even visited China. To me that seems horribly patronizing, even racist. China has such a rich and ancient culture, and truly wonderful folk tales of its own. That we are promoting and reading knock-offs is an absolute slap in the face. It's as if we are saying that what he wrote is better than what the Chinese civilization created itself.