In the Bug category, we just work with the fixed tag instead. A post saying something is a duplicate isn’t really solving anything, despite being useful, so I don’t think it would have been a good use there either.
Now, why we use fixed in some categories, and the solved-plugin in others, I think that’s probably due to what Moin already said. Tags are a bit more strict in use, so only the team can decide when something is fixed.