Student: Can you please edit my paper?

I have seen in my writing classes that students come into the class thinking that all I am asking for in their paper is "correct" grammar. In fact, every time I have conferences before a paper is due, that is their number one concern - if their paper is grammatically right? Or would I just edit their paper for them? Students who are not very comfortable with their writing often blame this discomfort on the inability to know things like comma usage, or subject verb agreement. I think most students are very conscious about their writing when it comes to grammar usage, sometimes to their detriment. I have had papers from students who consider themselves exceptional writers because of their grammar skills, but then I look at the paper and content-wise their paper has nothing. The students get so caught up in grammatical issues in their writing that they do not think that a good paper need more than just technically right (sounding) sentences. And of course, I am not placing the blame just on the students for their obsession with getting their papers edited by the instructor or the writing center tutor; this consciousness (whether good or bad) was raised in them for a large part by writing teachers. I do think that grammar is necessary for writing, but it cannot take the place of critical thinking. Micciche is right when he says, “The chief reason for teaching rhetorical grammar in writing classes is that doing so is central to teaching thinking." I really enjoyed reading Joseph M. Williams’ article “The Phenomenology of Error." I have often wondered if my English professor are reading my email and are cognizant of my "accidental" errors, and Williams' article explains the types of errors and the degree to which people notice it. I agree that we need to give our students some grammar skills that they absolutely need, but the more important thing is to make them aware of the errors that possible. I also think that each students level when it comes to grammar skills is so different that teaching grammar in a composition classroom can be very challenging. My question then would be--should we be pointing out grammatical errors in student papers?