I recall Frank did the Giro under protest. He and Andy (especially Andy) aren't motivated by anything other than the Tour. Frank will ride the Vuelta if he's crashed out of the Tour and give his best effort but how often will those circumstances repeat themselves? Andy's history shows that he really can't be bothered and really don't see that changing. Andy will continue to focus on the Tour and whatever team that has him will see him as their best chance at Tour glory. I think his time has passed. He will never beat either Contador or Froome and the young guns are rising fast.
Froome will win a grand tour before he retires. He has too much talent in both areas (climbing and tt) plus a strong team.
Rodriguez can but it will have to be either the Giro or the Vuelta. If he believes he has a chance at the Tour then he will be eliminating any hope of having a grand tour win on his palmares and it appears that his recent success versus Contador at the Vuelta and his near miss at the Giro has given him hope (unfortunately) that a Tour win is within his grasp. At his age I can't blame him for pursuing his dream and he's had a stellar career thus far inspite of his late start of being a team leader.
Gesink can do it if he focuses on the Giro and Vuelta same as Purito.
Samu can win a Vuelta or even a Giro but I'd say he only has 2 more years of productivity left. He came close in the Vuelta when Valverde won and always seems to bounce from one close loss in a grand tour, using it as motivation to try another one: Vuelta-Tour, Tour-Vuelta, never sticking with one. Being Euskatel's champion, he carries a heavy burden with Anton not coming close to his Vuelta performance (2010?).
The rest of those listed will be filling the grand tour gc standings as also-rans. They just don't have what it takes.