Confirmation by OP comment should be enough to close as duplicate
First, closing when the question has an accepted answer is not controversial: that’s the substance of the original answer.
Further, let’s note that closing based on comments is, in a sense, our current policy, as indicated in the linked answer. It’s true that it was edited in after most of the the voting was done (and probably should have been put as a separate question), but the answer has nonetheless retained its high score after that was edited in. Further, closure of questions based on OP comment acceptance has been going on at least since that edit (six months) with a minimum of controversy (i.e., no “reopen this question” posts on meta after a story-identification question was closed due to an OP confirming the answer to be correct in a comment).
Now, why do we wait for acceptance before closing story-identification questions? What makes them special (and what likely motivated the other answer in the first place)? It’s probably worth going to the second-most-upvoted answer on that page, which explains why we shouldn’t close without OP confirmation:
If we’re wrong, we’ve just annoyed the OP.
At best, we should try to guess what the story is – but only the OP
can confirm. We shouldn’t take that control out of their hands.
We want to make sure that the OP has a chance to confirm that a story is actually the one they remember. We’re not just trying to get an answer out there, or we’d close without acceptance.
If the OP confirms in a comment that the story is really the one that they remember, that’s at least as good as an acceptance. There’s always the (admittedly quite small) risk that a new user does not quite understand what clicking that checkmark means. But if they leave a comment, we can be reasonably sure of what the correct answer is. It doesn’t matter where they leave a comment: on the question, on the answer, or anywhere else. That tells us what the answer is, and that’s always been enough to close as duplicate.
And one other thing can’t be emphasized enough: there are a lot of people who come back, see the right answer, say “Wow, this is right, thanks!” and never return (and never accept an answer). Being able to close as duplicate in this case only makes sense: these are users that want to accept, but just didn’t know how.
In a similar vein, a self-answer is also sufficiently definitive confirmation that the OP has really found the work they’re looking for. We’ve closed in a number of those cases too, again pretty non-controversially.
Whether to comment or answer should be a matter of preference
With all this in mind, I don’t think we should be enforcing a policy of only answering and never commenting, or only commenting and never answering. Either an accepted answer or an OP comment is enough to close. While some questions, particularly those that are asked over and over with pretty similar descriptions, aren’t going to benefit from numerous copies of what’s basically the same answer, there’s always the possibility that a new answer might be better written, more comprehensive, or useful to a different segment of searchers than the existing ones. Both situations are sufficiently common that we shouldn’t say that one is always preferable.