Exactly!
This is such a tricky point I feel.
For example, it is in fact highly suspicious when there is uniformity of outcome in an “ostensibly fair” system. We should expect to be seeing the randomness of good luck, bad luck and personal choices in the outcomes. And to take it further, in a world that prioritises offering opportunity to all, this randomness should be uniform over all the various dimensions.
Of course back in the real world, it won’t be, because of inevitable systematic and random effects. And that is assuming we can even track and measure these subtleties.

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