I've been led to believe that the reason why a lot of written exams include the instruction "read all questions before starting on the problems" is due to this

I've been led to believe that the reason why a lot of written exams include the instruction "read all questions before starting on the problems" is due to this subconscious "cooking on the back-burner" effect. Problem solving in your sleep might be related to that strategy. I haven't read any empirical studies on the effectiveness of this testing strategy - but I suppose it should be fairly easy to set up such an experiment.