If one were to actually use this scheme for a class, I think it'd make sense to compute both the classical grade and the probabilistic grade and isolate student

If one were to actually use this scheme for a class, I think it'd make sense to compute both the classical grade and the probabilistic grade and isolate students whose classical and probabilistic grades differed greatly (as in your example of someone who answers everything correctly, but with low confidence). The professor could then exercise manual judgment to assign the appropriate grade and also probably discuss the discrepancy with the student (i.e., they might find it interesting that they consistently underestimated their knowledge of the subject; on the other hand, a student who was overly confident but did poorly might find it interesting that they were consistently overestimating their knowledge).