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I was under the impression that 是 was Chinese for "to be". The nuance isn't quite the same--you can say 是 in response to "are or aren't you American?", but that's more or less subject-omission--but it seems close enough?
But my experience with Chinese includes only two years of Mandarin classes and a few podcasts; I haven't studied the linguistics in so much detail, and that studying ended 5 years ago, so if you're basing this on something I don't know, I'd be glad for the correction.
I know much less Chinese than you do. Having said that:
The Chinese version of "be" lets you apply a noun predicate to your subject, but not an adjectival predicate: you can use it to say "I am a student" or "I am an American" but not "I am tired" or "I am tall;" that is, it doesn't state the attributes of a noun but an equivalence between two nouns. To say "I am tall," you just say "I tall." All of the other meanings of "be" (the ones relevant to this problem are those related to the essence/existence question) are expressed with various other words in Chinese.