While it is true that summing incommensurate measurements creates serious problems, summing ranks does not help. If the data cannot be summed, then that is the end of it. Any hope of a unidimensional ranking fails. No ranking reflects differences in degree. The heart of the problem with ordinalizing the data is that doing so strips out and throws away useful information about how much better one person or school is on some attribute.
Small differences loom large.
Consider also what could happen in a similar class the following year. If A and B do the same thing and C scores 2 points better on each exam, C goes from last to first place. Boy, C is flying now. Likewise with law schools. The changes, though perhaps truly random or otherwise insignificant, appear to be newsworthy.