Suppose that a court rules that one district must be re-counted, and based on the result there will be a new, random candidate.
This creates incentives for going after re-countings if your political opponent has won the lottery, not because the result will be much different, but simply because you get a second chance in the lottery.
It boils down to the thought that repeatability is import for fairness. Somebody claims that your DNA is identical to the one collected from the crime scene? You can make a second test and verify the first one. You think you have been treated unfair in court? You can repeated the trial at a higher court. All the doping tests in sports are verified by repetition.
The list is nearly endless. Even if a random experiment does treat you fair, you can't known.
The second point is that randomness only creates the appearance of fairness on the large scale, single individual still get treated unfair.