I think what you're talking about is already a thing. The text will be changed to "This question already exists", as shown in the image below.

Although the closure reason This question has been asked before and already has an answer. in the close dialog does not change, the publicly-displayed closure notice will indeed change to This question already exists instead of the usual This question already has answers/an answer here, as shown in the image below.

Therefore, I don't think this alone is a sufficient argument to restrict duplicate closing strictly to the case of actual duplicates. In addition, I am of the opinion that closing the repost as a duplicate of the original is more informative to viewers and also encourages the redirection of comments (and other activity) to the original question, making it more consolidated.

Unfortunately, in the vast majority of cases I've seen, the OP deletes the original question while making the repost, rendering normal users unable to close it as a duplicate of the original, so this is a really small subset of cases.