This is good and should be implentedimplemented.
I have some arguments and suggestions going towards the feature.
You are told that if your question is ever closed due to any reason even duplicate, you should edit your question so it fits all the criteria mentioned in the Help Center.
If this question can be reworded to fit the rules in the help center, please edit your question.
But if you are unaware that your question was closed in the first place, how can you possibly try to edit your question and attempt to make it reopened?
The system is also made as if this was already implemented and that it nearly almost requires this to function properly:
When someone closes a question as duplicate, an auto-comment is created, notifying the OP immediately
When someone closes a question for another reason and leaves a comment (optional), the OP gets notified instantly
Putting a question on hold before a final decision is best if the OP did his job of attempting to fix the problem in the first place
For those who constantly ask questions, finding whether one of your questions was closed or not can be a big problem or just those who don't even check the status of their old questions anymore... it's still a big issue.
For new users, it can be a great learning experience to rebound from their mistakes and create instead excellent new questions that are well-received from the community, something every new user wants here at SE.
For active users, you would be shocked to see your question closed and would be very eager to reword your question so it can fit the Help Center rules appropriately. But if you don't know it then trouble arrives...
For veteran users... well that's self-explanatory how shocked they will be.
The suggestions
Instead of only generating a comment for just a duplicate, why not create one for each closure reason. This will ping the OP when their question has a close vote for whatever reason, fix it appropriately, and no longer need lots of rep to see the reason for closure until the very end (if it is closed). The format could be like:
Cast close vote for {insert closure reason here}
Short, simple, self-explanatory, and is user-friendly. Another suggestion is so that Community posts a comment saying that your question has been closed:
Your question has been closed. Please edit your question so it will fit the rules of the Help Center.
The good
As new and veteran users network wide get these notifications, they will most likely edit their questions in an attempt to get it reopened and possibly learn from mistakes so that means:
Smaller Close Votes queue (Especially for Stack Overflow)
Less time closing, more time contributing
Moderators and users can take some time off moderating new users and their questions
Question quality goes through the roof
The bad
Of course, there will be the bad. Just imagine you are a new user with your first question with high hopes to be well-received by the community and you get a comment that crushes your dreams.
New users might be discouraged
New users are puzzled
The miscellaneous
Comments should also include some posts relating to creating good posts, such as the Help Center posts or Jon Skeet's detailed blog.