Of the two leading incomplete-sentence punctuation marks, ellipsis and dash, neither started out being used for the purpose. The older use of ellipsis is to indicate omitted text in a quote—the use of ellipsis to trail off is newer. Similarly, older dashes join clauses within a sentence, while newer dashes can be used for dialogue that gets interrupted.
So we’ve always had incomplete sentences, from truncated news headlines and standard trail-offs like “well…” or “but yeah” to more recent innovations like “because x” (because reasons, because yay) and “I can’t even”. Though, ellipsis, dash, and so on don’t have the exact flavor conveyed by final hanging but, or, so, or comma, so perhaps we were lacking appropriate words and punctuation to indicate “this is so obvious I’m not even going to finish the sentence.”
Where do trailing but, or, so, and commas come from? Some linguists think that final hanging but might be related to Japanese, where the particle kedo does the same thing, but that doesn’t explain the other three.