Major exams like the SAT or GRE are graded anonymously; info identifying test takers is hidden from test graders.  My department follows the same policy on its major “prelim” and “field” exams.  But in virtually every class, grading of homework, exams, etc. is not anonymous, even though that would be easy to arrange.  Yes class presentations and participation couldn’t be anonymous, but the rest could. Presumably the reason major exams are anonymous is to avoid even the appearance of the possibility of bias or corruption; why allow such an appearance with classes?

Also, letters of recommendations can be nearly as important as grades.  Yet most schools have zero procedures to avoid corruption there.  Students are given no guidelines or basis for comparison; no records are kept of who recommended who for what on what basis, so there isn’t any way to even look for corruption. Why so cavalier there?

Also, profs at top schools are advised to put minimal effort into teaching, as they will be evaluated mainly on their research.  So why do students pay extra to attend colleges with research-focused teachers who mostly ignore them?

As with docs and macro-economists, let me suggest people want to affiliate with prestigious others; a major product schools sell students is a direct relationship with prestigious faculty.  Anonymous class grading is avoided because it would reduce an important personal tone in the student teacher relationship; the possibility of corruption goes along with a personal connection.

Yes, colleges credential student performance, and those credentials would be more valuable if they better avoided the appearance of corruption.  But in addition to performance credentials schools are selling college students the ability to claim relationships with about fifty teachers, and to claim a closer relation with the few who write recommendation letters.  Perhaps students care about those relations nearly as much or more than they do about performance credentials.

Added: Schools also sell affiliation with other high status students.