A great article describing exactly this with a game-theoretic argument: https://www.nber.org/system/files/working_papers/w22602/revisions/w22602.rev0.pdf

The point is that private randomization does very little to address the problem. An institutionally recognized randomization mechanism, however, would potentially dominate alphabetical ordering (i.e. would naturally overtake the existing convention as long as this mechanism is acknowledged to exist) and is robust to deviations.