On one reason not to grade...

It presupposes a degree of maturity on the part of students, but the course with which I am still associated, operates only on a pass/refer basis (one opportunity to re-submit referred work; fiture at that point is failure and requires a re-take of the whole module, at best). Many students don't like it--particularly those who are themselves graduates and have a long history of assessing themselves by their marks, often of course relative to their class-mates.

The situation Mary Beard describes in the linked post is one reason (and it is incredibly time-consuming to adopt her solution, particularly for big courses).But it goes a bit further than that.

Let's apply the Dale/Bruner “Cone of Experience” to the situation--slightly odd, but it fills the bill and such tools are never more than pragmatic devices. In terms of assessment;

• what the students actually know/can do etc. is at the enactive level. It's real life. It's incredibly rich and complex and inherently unassessable because of that, so
  
• we devise means of assessing which necessarily lose a lot of detail in order to be manageable. Sometimes the detail we actually lose is precisely what we wanted to assess in the first place, but we just get it wrong. This is at the iconic level. The students do the assessment, but in order to compare them against a standard, or even against each other, or previous performance...
  
• we have to assess the assessment, and that gets even more abstract and symbolic. And attaching a single number or letter is as abstract as one can get (apart of course from manipulating those number mathematically) --or in other words loses the most information.

Assessment is always a lossy process, but numerical marking exacerbates the situation. That magic number is a distant and distorted proxy for the blooming buzzing complexity (if not confusion) of the student's experience and conduct; which moreover obscures that enactive level. We have made grades etc. so central to a mass education system (no, I don't know the alternative either) that once one has been issued it is almost impossible to get through any more sophisticated message to the student;

"Yes, it did only get a C+, but that was solely down to those daft mistakes you made with the statistics; if you'd got them right it would probably have been an A-"

"Yeah, right..."

Such practices are actively inimical to effective feedback and assessment for learning, in the current jargon.