Wu (1997, page 158) has "been unable to find real examples" of non-binarizable cases, at least in "fixed-word-order languages that are lightly inflected, such as English and Chinese."
to see why this is, observe that each rule of the form A → B C that has complexity no greater than k can be written using a string of k e < k indices into the target nonterminal string to represent the spans' boundaries.