Describe a common situation where there is clearly more utility in stating x bluntly than stating x politely.

Here is a fairly narrow one: when you are correcting someone who has made a serious error which they will immediately recognize as an error when it is pointed out to them.

An example took place earlier here on this thread. Lionhearted had just stated that he would bow out of the discussion now. Wedrifid misread what was written, seeing "I'm bowing out for now", where lionhearted had actually written "I'm bowing out now". Wedrifid responded intemperately, making a particularly big deal of the withdrawal "for now", interpreting it as a kind of threat to return. (This comment has since been deleted by its author.)

I pointed out wedrifid's error bluntly, and was even so discourteous as to tease him on his embarrassing error. I am confident that this was the right way to handle this kind of mistake. Anything softer would have been condescending.

So that is one situation where bluntness strikes me as clearly best. But I'm not sure that this situation generalizes well. If the mistake were less serious (a typo, say) then the superiority of bluntness is debatable. If the mistake were less clearcut, then it would probably be wise to include some justification of the judgment that it really is a mistake.