Close flags (those in the "it doesn't belong here, or it is a duplicate" category) are arguably the least important flags. A healthy community can usually deal with closing questions on their own, getting the moderators involved mostly just speeds things up.
I think that it would make more sense, and also be more consistent, if instead of close flags users below 3k reputation would have the ability to suggest closing a question analogous to the "suggest edit" feature. This would also put the question into the close review queue, but it would not put it into the moderator flag queue.
I think moving this ability would help to emphasize that closing is the job of the community, and not necessarily of the diamond moderators. It would also avoid filling the flag queue with stuff the community can handle itself, leaving the moderators to handle the more exceptional flags.
The core of this feature request is not new, the idea to not show the close flags to moderators (at least on SO) has already been discussed. But I think that also changing them from flags to suggestions makes it clearer what flags are actually meant for. By removing the part that the community can handle itself, the purpose of flags as a way to call a moderator is made more obvious.
Of course sometimes the moderators also should or have to close questions. This is especially common on smaller and new sites, where the community can't manage this alone. So the close review queue should be improved to be useable for mods, or maybe even visible in the style of the flag queue for moderators in an optional view.