I think this can be easily solved by changing the way option(s) are given to choose when OP decides to close his own question. After all, it's the OP who wants to close the question. I can understand keeping the question open so that enough voters can agree upon the reason for the close in case of the other users who flagged the question as a duplicate. But, here it's the OP who is actually casting a close vote.
But, if the system is designed (see Note at the bottom) to ask for the confirmation/reason for the close, then how about making a little change (as suggested below) in the dialog box when OP (as the system can detect or already knows the owner of the post) decides to close the question.
As per the OP quote:
"Someone voted to close my question as a duplicate. I agreed, so I cast
my close vote (I have enough reputation to vote to close)".
Based on the facts, i.e. :
- OP (the owner) wants to close his own question.
- OP has enough reputations to cast his close vote.
- System recognizes (by detecting) it's the OP and not any other user.
Everything below only applies/valid for the above given facts.
Now, upon clicking the 'close' link under the question body, OP is given the options list as shown below: (Image taken from the Help Center > Privileges > Cast Close And Reopen Votes)
I would like to suggest the following change(s) to the above shown options window:
We could add a button anywhere in the bottom (may be next to "Vote To Close" button). Here, OP can cast his vote by selecting "duplicate" radio button from the options list and then clicking the "That solved my problem!" button. This should close the question immediately. Whereas, selecting a "duplicate" radio button from the options list and clicking on the "Vote to Close" button will just cast an ordinary close vote.
Alternatively, we could change the "duplicate" radio button title as "duplicate... and it solved my problem!". Now, OP can simply select this radio button from the options list and click on the "Vote to Close" button to cast his close vote. This should close the question immediately. No need of "That solved my problem!" button.
With the implementation of any of the above given suggestions, it is possible for the OP to close the question immediately without needing an additional confirmation shown afterwards in the banner at the top. It will surely avoid the confusion that OP witnessed here in this particular case. I'm sure there are few more other possible ways this can be implemented, but this is what I can think of. Please share your thoughts, ideas any suggestions.
NOTE:
I am assuming this belongs to the status-bydesign category. Also, the close vote will not work (status by design) if there's an open bounty on the question. It would be great if someone from SE team (or moderators) could share more details on this.