Well the guy did - as observed - co-write the screenplay to Skyfall, so I kind of assume the positive reception that film has got is what he's making his case with. Yeah, Nemesis sucked, and maybe he wrote bad dialogue in Gladiator, but he's not fishing for the job of Gladiator II or the next Star Trek movie.
Rumours are starting to circulate that the Damon Lindelof and Brad Bird's top secret project "1952" that they recently, supposedly, "brought to Disney" and was intended as a tentpole, franchise, theme park and merchandising extravaganza is actually Episode VII.
Interesting rumour. As I said upthread, my only concerns about Bird are how well can he transition to live action filmmaking. Ghost Protcol is okay, but it's not exactly the brilliance of Incredibles or Ratatouille.
On the other hand given the huge amounts of CGI your average Star Wars film uses he's halfway there already (although there's some interesting articles on how Stanton's work at Pixar did not
prepare him for the transition to a live action schedule, so there's that.)
As for Lindelof don't know him beyond Prometheus, which I did generally like. The only big issues about that film was its somewhat convuluted handling of its central mysteries, and since a Star Wars trilogy is unlikely to build itself on Big Mysteries like that (one assumes), that may not be a problem.