This makes a faulty assumption that all OPs are responsive and even look at these things. This is especially the case with a myriad of duplicate questions that are migrated to Meta, where the original author doesn't bother to come register here. This also assumes that all OPs are responsible and will understand when an appropriate duplicate arises. Like you said, some people get offended at the concept of having their questions closed, so even when it fundamentally is a duplicate, these people will use every possible content difference ("I asked about posting images, that post is only talking about posting screenshots!") to keep their question open.
The author of a question is not necessarily the authority on whether that question is a duplicate or not. That does not mean that the community is always right and they are always wrong - it is perfectly acceptable to appeal closings, which is why we have the reopen process in the first place. But the best way to get your question reopened is to be civil. If you're civil about it and can clearly explain why a question is not a duplicate, you stand a chance to convince people that your question deserves to be reopened.
Restricting the approval vote of duplicates to the OP and moderators, noting that duplicates are in fact one of the largest problems we have, would be rather damaging to the system. Yes, we might reduce the number of closings of questions that would need to be reopened, but you also will reduce the number of closings of questions that need to be closed. And there are a lot more of the latter.
I'm not saying that the OP is always going to be of bad judgment here, but that being the author of a question does not grant the OP any better judgment than the rest of us. We're not faultless either, which is why it isn't a one-person process for the community vote. If the OP (or anyone else, for that matter) can explain the case convincingly, and there are many good cases out there, the question can end up reopened. Since the vote-to-close as a duplicate generates an auto-comment identifying the vote, it's even possible to halt the incoming votes, and if you're convincing enough even the people who originally voted to close will vote to reopen if it does unfortunately get closed. Remember that the community can disagree with a closing proposal just the same as they can disagree with reopening (and speaking from experience, it is beyond amusing to have a question that should be closed as a duplicate and have it left open).