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I agree with you on this. Arbitrariness and justice are incompatible. And I think the incompatibility runs deep. It is part of the concept of justice that it is opposed to arbitrariness.

The philosopher Chaim Perelman talks a lot about this. He points out that not only do we think that equal cases should be treated equally, but when cases are unequal, there should be a certain proportionality between the difference between cases and the difference between the benefits or burdens they merit.

For example, if one man steals $100 and is given a year in prison and another man steals $100,000 and is given 18 months, we say that the proper proportion has not been observed. The difference between the cases and the difference between the burdens is not the same. And because of this lack of sameness or proportion, we would say that the decisions were unjust.

Again, trying to achieve this proportionality is a way of trying to eliminate arbitrariness from decisions.