We encourage users to explain what they've tried, what didn't work.
In the case of something like your example:
CLOSE VOTERS: please don't close this as duplicate because it is not because A,B,C.
That is exactly the sort of thing that should be in the question. All they're really doing is telling people what they've tried before. Or how their question is different. These are important things to know.
The phrasing might seem conversational or combative, but notices like this usually crop up after some close votes have been submitted. I know some of the other answers here have said that closeClose votes cannotcan be retracted, and that is true, but more importantly having any close votes means you're exposed to the close vote queue.
So once it's in that queue, that a message like this stands out is a good thing. People have a habit of auto-modding their way through the review queue and this it just the sort of thing that might catch their attention enough to pause and investigate. Obviously if they disagree, they can leave a comment explaining that and vote to close.
The only downside of any sort of post notice is it looking a little crufty, but at the same time the it's not unreasonable for you to not want youra question unjustly closed. The amount of effort wasted in closing and reopening that is far more costly than bearing a notice for a few days until it leaves the close queue.
I don't disagree with Kaz's point about working these differentiations into the post, I just don't think that also making a song and dance about it as a very visible aside is always a bad thing. Some differences are very subtle and need explanation.
I also don't think it particularly bad that other people edit post notices in, where required. Collaboration works in all directions and again, highlighting technical subtleties for reviewers could save everybody a lot of time, confusion and frustration. It might even get their problem solved.