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While I'm no major supporter of WPA, I do believe that there are potential uses for the approach that 'might' be able to shed some light in areas not yet plumbed.
In general I agree that WPA is effectively useless in a predictive way, (other than it tends to capture the best hitters as best and worst hitters as worst - just not as well as other advanced stats). 
I think the assessment "Boy, did so-and-so do great for us this year," is exactly the right frame of mind when seeing a particularly awesome WPA.  In a sense, WPA is the *ONLY* stat that in some way actually captures "the double".  There's some value there, I believe -- though I think at present WPA is mostly misused.
That said - I just had a brief exchange with the patron saint of WPA, (Pirata), posing the idea that WPA might be a potential tool for examining Arm ratings for OFs.  You might uncover that some (most?) OFs generate their assists when trailing by 5 runs. 
In point of fact -- WPA might be a methodology to utilize in examining defensive value.  If you are constantly in 1-run games, then the value of every defensive play, (good or bad), is sky high.  And when up by 8 runs, it's to be expected fielders might slack off and allow some extra hits.  Maybe Jeter's historically poor range values are 'tainted', because he was often playing when leading by 3-5 runs. 
It might reveal nothing.  It might show the same lack of predictability that offensive WPA tends to show.  But, there's always the possibility that something new might be revealed.