Yes, that sort of mirror-sampling would reduce variance. The problem is, though, you need to know all the uses of randomness in order to properly counterbalance

Yes, that sort of mirror-sampling would reduce variance. The problem is, though, you need to know all the uses of randomness in order to properly counterbalance them, and these systems are already enough of a pain to use. (For example, if you have two, you can simply swap: but what about other biases? like if it's broken in half to assign to 2 grades. Or what about if there are three exams? And what about balance across other courses? if you want to do variance-reduction and tricks like antithetic sampling, you need to know all this in order to structure it properly - get it wrong, and you may make things worse.) So that's why simple random shuffling would be preferred. It allows total ignorance of all other uses (past present and future), handles all ordering biases, and can be done independent in parallel across arbitrary sets of courses/exams/grades/students.