Grades as Feedback

In Alfie Kohn's article, he discusses the use of grades as a way of giving feedback, but not as a way of measuring knowledge or success. Kohn advocates that grades are a good way to give a student feedback as to what he/she has yet to master and what areas he/she should work on.
This idea left me wondering how grading for feedback would actually work. Why use a number or letter grade to give feedback, when the student would benefit more from written comments or one-on-one discussions with the teacher about his/her progress? How would this feedback then be used? If grades are irrelevant, then the student would not use the feedback to boast the quality of his/her grade. How would a teacher then assess whether or not the student is actually using this feedback unless the class was given some sort of assessment exam? Perhaps I am over-thinking Kohn's idea, but I'm afraid I don't see the merit of his argument.
I do believe that feedback is important, though. For example, in an essay-writing course, comments on rough drafts guide students so they can produce their best possible work. This work, however, must be assessed somehow to assure that the student has been heeding the advice of the teacher.

My question is this: Can you think of a situation where a grade for feedback purposes only would be useful without a subsequent assessment or opportunity to show that the feedback has been put to good use?