Think of it this way. The article presents a random-gap list with only five entries, and it looks terrible; the most common page occurs 9 times as often as the least common.
Now think about a random-gap list with five million entries. With that many entries, will the gaps balance out? In the best case, five of them end up in the range from 0 to 1 millionth, five of them end up in the range from 1 millionth to 2 millionths, etc. But we've already seen what it looks like to have five uniform random numbers in a range (whether it's big or small doesn't matter); the gaps tend to be really varied. So we're going to get this sort of imbalance between gap sizes (viewed as a ratio) no matter how many entries we insert.
One other thought experiment: the article mentioned a page with a gap size of one billionth. How many pages will it take for that to balance out so that page doesn't have an unusually small gap any more? How many pages does Wikipedia have?
(This is similar to the reason that infinite space packed with marbles has the same packing density as infinite space packed with bowling balls.)
Now think about a random-gap list with five million entries. With that many entries, will the gaps balance out? In the best case, five of them end up in the range from 0 to 1 millionth, five of them end up in the range from 1 millionth to 2 millionths, etc. But we've already seen what it looks like to have five uniform random numbers in a range (whether it's big or small doesn't matter); the gaps tend to be really varied. So we're going to get this sort of imbalance between gap sizes (viewed as a ratio) no matter how many entries we insert.
One other thought experiment: the article mentioned a page with a gap size of one billionth. How many pages will it take for that to balance out so that page doesn't have an unusually small gap any more? How many pages does Wikipedia have?
(This is similar to the reason that infinite space packed with marbles has the same packing density as infinite space packed with bowling balls.)