Faery tales are funny things that never quite die in the collective consciousness. The same applies to folk tales and classic mythologies.
They may get reimagined, reworked, rebadged, but the common core remains in the foundations of a culture.
This is not to accuse anyone of plagiarism, or even of unoriginality, only to acknowledge that there are cultural influences that may manifest in unexpected places.
It isn’t something I would have noticed before, but watching Sailor Moon Crystal with friends has suddenly brought the similarities to mind. E.g. Kaguya-hime is a princess from a moon kingdom and the tale contains elements of lost memories, and forbidden (or at least discouraged) romances.
Sound familiar? Having seen the first 8 or so episodes of Sailor Moon Crystal it is certainly sounding familiar to me.
Given that Kaguya-Hime is considered the oldest extant Japanese narrative it doesn’t surprise me in the slightest that it, or aspects of it, manifest in odd or unexpected places in anime.
I’m left wondering how many other anime have had elements of The Tale of the Bamboo Cutter. More interestingly, how many have had elements that I did not recognise out of cultural ignorance?
I’m betting that the answer to that question is: a lot.
Feel free to sound off in the comments with suggestions.
 I still haven’t seen much of the original Sailor Moon. I mostly skipped it at JAFWA.
 See the Tale of the Bamboo Cutter Wikipedia link.