Plus, its not the ideas that make or break the story, its the execution.
I agree that the premise of both JJ movies sounds like bad fanfic if presented as a brief summary. But that's not really the writing, that's just the idea. The execution was pretty darn good and I think in both cases they somehow managed to pull it off.
I had a lot of problems with the first movie (mainly, the characters - I wanted more warmth and humor and interaction there. Too many felt like caricatures rather than characters.) The second movie was much better in that regard! Or maybe I'm just marveling at how Kirk / Spock / McCoy worked - and Kirk / Spock / Uhura worked even better.
As for Khan - I didn't like the idea when people first started talking about whether they might have Khan in the film, years ago. But (to my surprise) it worked, at least for me.
I still think making this particular Kirk a captain with his life experience (or lack thereof) is stretching believability pretty thin. In the TV series universe its pretty clear that he's had years of experience in space, with prior postings, and that he's qualified to be a starship captain. That's really my only ongoing gripe with the new movie universe. But the movies are a lot of fun despite this, and Chris Pine is so good in the role that he makes it work.
I'm excited for the next one. Five year mission? I hope they're "boldly going" in the next one and not just saving earth from yet another villain.