As mentioned in some of the existing answers (which annoyingly I'm unable to comment on), the problem is that x++ ++x evaluate to different values (before vs after the increment), which is not obvious and can be very confusing - if that value is used. cdmckay suggests quite wisely to allow use of increment operator, but only in a way that the returned value is not used, e.g. on its own line. I would also include the standard use within a for loop (but only in the third statement, whose return value is not used). I can't think of another example. Having been "burnt" myself, I would recommend the same guideline for other languages as well.
I disagree with the claim that this over-strictness is due to a lot of JS programmers being inexperienced. This is the exact kind of writing typical of "overly-clever" programmers, and I'm sure it's much more common in more traditional languages and with JS developers who have a background in such languages.