As a general rule, NO.
There are specific instances where a question is on-topic for multiple sites and you wish to garner answers from different perspectives. But note that if your question is so broad and nonspecific that it can be asked without change on multiple sites, there's a pretty good chance you've abdicated responsibility for asking a good question in the first place: seeing your question closed as "Not constructive" on multiple sites isn't going to make you happy!
So in these (rare!) cases where it seems appropriate, do not simply copy the question verbatim from one site to another. Tailor it to the audience you are addressing, and ask for the type of answer you wish to receive.
For the example given ("Why is literature translated from Japanese always so 'clunky'?"), it's clear to me that this question was written with the Literature.SE audience in mind: a general observation is made and then solidified by referencing a specific author's work, the specific question is for references to existing discussions of this perceived phenomenon, and only at the end are specific examples of wording / phrasing given.
Assuming any of this is on-topic for this site, my guess is that they would be the implied cultural aspects and explicit examples of word-choice / phrasing. Reworked to emphasize the areas that are the specialty of the experts here could produce a rather different question... albeit one on the same general topic. And at that point, what you're doing isn't really "cross posting" anymore!