The option is good. Even if 90% of posters won't close, the other 10% might be sensible and close the thread.
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Oh please no. The forums are a place for discussion, and I frankly don't trust the general forum population with the power to shut down their own threads. Forum mods are at least somewhat accountable for their actions and follow a fairly clear set of guidelines (forum rules), ordinary members would have no such restrictions (and are less reliable in the first place). I have no doubt that many people would use it appropriately, but there's that fractuon of people who wouldn't unfortunately.
And I can assure you asking the mods to close a thread for you (and others who want theirs closed) would be much easier on the mods than getting all kinds of complaints and questions about inappropriately closed threads that they had no part in (also remember if they leave no closing message you can't even tell if a mod or member did it).
No, we require a permanent sign of the OP's stupidity for all to see
Also.. many people have temporary threads(How should I attack this war base, general questions about the game, etc.) Just clearing out a few of these would be helpful for the forums.