There seems to be an undercurrent of indignation, as if there was some kind of criticism involved in talking about an odd quirk of nomenclature, and some need to defend the right of people to use the term "American" to refer to themselves.
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There's a distinction between Yank and Yankee in the way it's used. The latter is pretty widely recognised here to refer to people from part of the States, even when we might not be sure quite which part too precisely. The former is pretty universally used to mean "Americans" generally, without any connotation of hostility.

Of course you have Yankee used that way sometimes, as in Cyril Tawney's song "Sammy's Bar", with its fatal "Yankee Car", but Yank wouldn't have scanned.

South Americans have different rules, with "Yanquis" meaning all "Americans", frequently enough a degree of rancour.