Do we know how much involvement J.J. had with the story or script for either of the first two? He didn't receive story or screenplay credit, though admittedly that could be simply out of generosity rather than a reflection of the work he did/didn't do.
Well, in Hollywood movies, the director is always the ultimate arbiter of script content, with the writers' job being to give the directors what they ask for -- which is why so many movies credited to talented screenwriters end up being incoherent messes, because a lot of directors are more interested in the visuals, acting, effects, and every aspect of filmmaking except
plot and dialogue. And which is why it's a good thing that more and more film directors these days are coming from the ranks of TV writers/showrunners like Abrams and Whedon. And I assume Abrams's relationship with his ST staff is the same as his executive-producer relationship with the showrunners of Bad Robot's various TV series -- he supervises the process and has input into every decision -- but with the added layer of control that comes with being the director.
Honestly, I'd almost think it should be the other way around - it'd be easier for a director to punch up weak dialogue on the set, but if the story's not strong then by the time they're involved it's too late.
But as I said, in films the director is always the ultimate guiding force behind the writing process, whatever the credits say. The story is shaped to the director's specifications from the word go. So having a director who's also a writer would be the best chance of getting a solid, coherent script.