I concede my terminology is anti-convention, and "wrong" (with respect to convention) BUT I disagree with you here:
If you were given a sheet of paper a week ago, with only the phrase "a fully DC sine wave" on it, and you were asked to come up with as many realistic possible meanings, I have to believe that you could have only come up with one (and rather quickly)
If true, then your statement:
communication with others.
would hold true about "a fully DC sine wave" with respect to convention/"old definition" but not with respect to "communication" or ambiguity....while not "pure" or conventionally correct, is there really any other possible interpretation of "a fully DC sine wave" and therefore wouldn't you agree that being a "hyper-stickler" on this point is really not justifiable?
Again, isn't there more ambiguity (poorer communication) in your description:
AC-component
versus:
a "fully DC sine wave" versus "a partially DC-offset AC sine wave"