Assessing a penalty for inquiries regarding exceptions to deadline policy My problem: Though it's made explicitly clear to my students that I do not accept late work and do not grant extensions, I get at least 5-10 e-mails a week asking about extensions. I want to deter these emails, I feel obligated to respond, but my response is usually "See the syllabus regarding missed assignments". Dealing with this is costly in terms of time spent replying and clearing my inbox.

I make it very, very clear in my syllabus that I do not give extensions for assignments under any circumstances except limited administration excused cases and that I will not respond to requests (a blatant lie, I do respond because I care what they think of me and the course). I remind my students at the beginning and end of every class of their impending deadlines. I also regularly remind my students in class that deadlines matter and there are no extensions and no late work. My assignments are brief, and are available for over a week for the student to attempt, I don't feel my demands are unreasonable. I stress in the syllabus and in class that the way I accommodate the various life issues that cause missed deadlines is that I will drop their lowest X assignments, where X is a very generous number 

My question: is it unfair of me to put a syllabus clause that specifies a minor penalty for e-mail inquiries regarding an exception to the deadline rule?
Something along the lines of "Each e-mail inquiry asking for an extension on a late assignment may be subject to a Z point penalty on your overall homework grade" where Z is not an unreasonable number.

Would I be a total jerk? Is there a better way of solving my problem?
A colleague had a phrase along the lines of:

"Any email question or request that is already answered in the course documentation will not be replied to".

Seemed to work well for him.

But I would not do any type of downgrading for that.

Students do talk to each other and it soon gets around "well don't send that, as it won't be answered.."

Relevant questions that did warrant a response did get answered to the student and, sometimes, repeated to the class as necessary.