We can combine your two observations into the same query, thus:
And while kinky has been more common than either Kinki or Kansai in English, the rise of kinky does seem to correspond with the decline of Kinki pretty strongly.
Other factors could include earlier texts being more likely to have one misread by the other by google's OCR, but it seems a reasonable conclusion.
Quite aside from the connotations being inappropriate, avoiding homophones is always a reason to favour one synonym over another.
Others though include the simple fact of which is more often seen by readers leading words to be one of the cases where nothing succeeds like success, or the simple fact that the latter just looks more Japanese to an English-speaking reader. Certainly, I immediately thought that Kansai looked like a Japanese word, but didn't have the same reaction to Kinki, so that would be a reason in itself to favour it for an English-speaking audience. Connotations will still help too of course (I don't care how many relatives my partner has called Bent, I'm not naming any future son that if he's going to live in an English-speaking country).
However, "関西地方" gives me more google results than "近畿地方", and while some are clearly google knowing they're synonyms, that does suggest that Kansai is more popular than Kinki in Japanese too, which would hence be a source of comparative popularity when used in English.
It's possible that knowledge of the English has even affected the Japanese preference, though we'd need similar data in Japanese to even begin to judge the possibility.
So in all, I think we can say that the similarity to an English word is certainly a very plausible as a reason for favouring one over the other, but it's not proven, and certainly not proven as the only reason.
