My medical school, like most top medical schools, did away with grades in the first two years. Every student does take the same class from the same professor. The professors can still calculate an ordinal rank order of the students because they have all the test grades. And it's mostly trivial anyway because the residency programs aren't nearly as interested in your grades as they are in your standardized test scores.

The only thing that happened when we did away with grades was that the students lost the only quantitative feedback they had. We even had professors in the beginning refusing to give us our test scores.