I don't know about that. Taken to the logical conclusion, wouldn't that mean we should teach Chinese history in Chinese? Mentioning that other cultures see time differently - sure. But using those systems exclusively when speaking of that culture ... I'm not sure I see the point of that. The text for my Chinese history class was from Jonathan Spence, considered the western expert on Chinese history. In his books he insists on using the modern Chinese transliteration of names and terms (so Peking becomes Beijing, etc.). I understand that to some extent - people should be allowed to define themselves as they see themselves. But the new transliteration is a somewhat silly political maneuver whereby the Chinese attempted to throw off British influences on their culture. That silliness is exemplified by the transliteration of Qing. The old British system rendered it Ching, which is pronounced "ching". In contrast, the new transliteration is pronunced "ching" ... uh. So the Chinese replaced the "ch" with "q", and then changed the pronunciation of the English letter q. Hmm.
I get it that the actual Chinese word is neither a pure "ch" nor "q" sound, but that's just odd. They're offended that the British appropriated their words and anglicized them, so they transliterate all their words in a way that appropriates the English alphabet and introduces new pronunciations that the Brits don't use, that doesn't reference the actual Chinese system, and thereby creating a useless set of characters that neither the Chinese nor the British understand. Oy vey.
History, by its very nature, is a process of translating the experiences of other people into terms that we can understand within the context of our own experiences. So, if we're going to translate Chinese history into English, I've no problem using terms that English cultures will understand - dates and all - with one caveat: that we are careful not to stuff Chinese history into an English framework.
With the exception of the one little oddity I mentioned, Spencer successfully does that. My Chinese history class was the first I ever took wherein I had the odd feeling of separation from the subject matter due to unfamiliar cultural paradigms. I had to work really hard to overcome that. With great effort, by the end of the class, I felt I was finally beginning to see the world as the Chinese saw it - though admittedly my view was still "through a glass darkly" (to quote a famous passage you're probably familiar with).