I don't understand why lottery are used so much in official context. Instead of the best, you select randomly and hoping RNGesus is on your side. I agree about the threshold, but how about using other criterias instead of RNG.
Not only do lotteries mitigate Goodhart's Law (which rewards 'bad' candidates who appear good, whilst punishing 'good' candidates who don't appear that way); but even a perfect, un-gameable measure can waste resources chasing diminishing returns. Even something as trivial as spelling mistakes can be decisive; and whilst those judging might only care a little about spelling, candidates care a lot about winning, so it's in their interest to obsess over even such minor things.
This imposes a massive opportunity cost, whether it's spending whole childhoods in 'cram schools'; or university salaries going to 'grant proposal writing services' rather than educators and researchers; etc.