We don't mark on paper!
I believe the protocol is that a professor must collect the printed exams.
The box remains sealed until shortly before the start of the exam. The box contains all the exams, a form on which we have to specify how many of the printed exams were filled in and how many remained unused, and a different colour seal that we must use to seal up the box once all the exams are returned to it.
Then any education-related employee can return the box (as long as they have legal ID and an employee card).
The exams are then scanned and uploaded to a marking interface. The MCQs are marked automatically, and all empty answers are marked as 0 points.
We can then easily short-key our way through the answers provided by the students, marking one sub questions at a time, so there's minimal context switching and, ideally, maximal fairness b/c the same person grades the same sub question for everyone. This also allows for easy parallelisation during marking.
Once all the marking has been done, the interface computes statistics about all the questions, so we get some sense of the correlation between getting a question correct and passing the exam, and how easy or difficult each sub question was etc. If it did end up such that multiple people marked the same sub question, we also get stats on how they differed on how many points they awarded on average, so we know when to do an extra check for fairness.
Obviously how informative these stats are depends on how many students took the exam.
I do quite like that this system makes it so that I never have "naked" exams in my office that I have to guard, and the marking interface is super convenient.