The only way pseudo RNG would make the game non-irritating would be if the “bad luck insurance” worked such that each attempt increased your odds significantly of getting the reward. So if for example the initial drop rate was 5% (1 in 20), the second attempt for a player the drop rate would be 10% (2 in 20), the third 15%, and so on. The idea being that if it were a 1 in 20 drop rate, then at least if you run the thing 20 times you are guaranteed a drop.
And yes, I understand this is totally not how the laws of chance work, but Blizz already claims they have some sort of bad luck protection for certain drops, why not make the algorithm mean something and at least give those with chronic bad luck some hope?