I would also like to point out that the poll and the OP doesn't distinguish if we're working within a fixed, or variable comparison here.
If we're playing a low-magic, dark-ages, grim and gritty system, we're shooting not only for a lower bar, but also an entirely different goal post here. Low numbers work because it's more representative of how difficult and cruel life is. You live or die by the chance of any given die, but are more likely to come home beaten, broken and bruised than outright dead, then you get some horrible disease, linger for a few weeks, possibly infect your family/town and then die horribly anyway.
If we're playing a high-magic, super-heroic setting with all sorts of powerful and incredible beings, we most likely have a higher bar, but again it's a different goal post. Here high rolls represent how awesome and incredible you are, how much above the prior example you the hero(heroine) you really are! You can call forth lightning from your fingertips, engage in great duels of honor with legendary warriors. You are less a subject to the die as one who has mastered it and uses it to their advantage.
In the first, low numbers are good because they are fitting, just as high numbers are good in the latter for the same reason. You wouldn't want huge numbers in the former because it would take all the style and grit out, and you wouldn't want low numbers in the latter as it would take away from the awesomness.