Great! This is getting closer to a testable hypothesis. I’m imagining “students chosen randomly from the applicant pool, and students chosen based on merit will have indistinguishable academic results”. This isn’t perfect yet but it’s closer to being testable.

However, my hazy understanding from psych lectures years past is that similar experiments have already happened and the results are in. University achievement was found to be correlated with big 5 consciousness and IQ. (I can’t remember the effect sizes.) I have no idea how well the US collage admissions process selects for those traits. I’d love to be proven wrong, but I would bet money a lottery would lower the average academic achievement of collage graduates.

(Edit: first result on google scholar talks about the positive correlation between GPA and consciousness: https://onlinelibrary.wiley.com/doi/pdf/10.1002/per.732 )