I totally agree. To be fair about OldSpock in STID, while a chorus-like scene in which a character explicitly explains something is problematic few sci-fi and superhero movies can do without one. Furthermore a movie can be good without Khan being brilliant (otherwise TWOK would not be so popular) and of course your previous point is totally correct, Khan simply kicks a*s in the scene with the Klingons. We cannot pretend that Space Seed is not the eternal benchmark* for Khan but this does not mean that a Khan which differs from the original character setup is automatically bad.
Khan's lack of backstory and out of the blue appearance in STID is perhaps also partly due to Abrams' mystery preferences (which also influences the visuals, e.g. Qo'noS is quite opaque and maze-like in the D4 hunt scene). A character is after all not a fixpoint, unchangeable through all the stories in which he or she appears, but subject to all kind of influences. Kirk, initially designed to be no difference to the contemplative Pike but then influenced by Shatner's energetic acting, is probably the best Trek illustration of this.
* - When we hear Khan the first thing which comes to mind is most likely him reciting Melville and while this is his undoubtedly his most intense and beautiful scene it is not a quintessential Khan scene just like Picard's Moby Dick scene in FC is not defining who Picard is. The very use of Ahab in both cases rather shows that it is atypical, being destroyed by a hunger for revenge is a universal issue and not Picard- or Khanesque.