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This is a classic!

A, B, C, D, F

4, 3, 2, 1, 0

exemplary, excellent, satisfactory, acceptable

does it really matter?  Its this a Potato/potatoe issue?

You say "'A' seems very quantitative" ... really?  I would argue that I really hate lumping all the students who EARNED a grade in the 90-100 range because it equates those who earned a 90.001 with those who earned a 99.999.  I do not think that is fair and certainly these students are at different levels and not just an 'A.'

I also would argue that having more steps (like A+,A,A-,B+,B,B-,...) is NOT the solution.  If this were the case I would simply argue to stop all this subtrafuge (Wil's word) and just give the numeric grade that the student earned.

I really think the answer is to grade each student NOT on an absolute scale, but on a PERSONAL relative scale.  This involves a lot of work by the teacher to really know each student's capabilities, strengths, and yes, content knowledge .. then grade each on their personal growth (progress), personal strategies (process), and personal work (product). 

Why do most of us associate differentiation with instruction?  I say differentiate EVERYTHING ... including assessment.