Wilford Brimley did not receive an Oscar nomination for portraying Ben Luckett in Cocoon.
There is of course Don Ameche's Oscar winning but not particularly interesting story about getting married that really does not go anywhere special. Hume Cronyn somewhat interesting story about his character going back into old bad habits after regaining his youth. There is the rather short, but moving in the pivotal moment story involving Jack Gilford whose character refuses to use the pool even for his dying wife believing that that it is entirely unnatural. Then there is Brimley's story involving leaving his grandson to go with the aliens to live forever.
Brimley actually only has a few scenes where Ben spends time with his grandson, and really the importance of the scenes does not come until one near the end of the film as they fish together. There scenes before this one are nice as they show warmth together, but the power really comes in the fishing scenes where Brimley shows Ben trying to tell his grandson that he is going away. Brimley is very moving in this scene but really because he does not push the emotion. Brimley allows to come naturally in the scene as he calmly explains why he has to go even well still showing some regret since he must leave his grandson.
Aside from that scene though Brimley does an excellent job of standing out the most out of everyone within the cast as Ben, who although enjoys the rejuvenation stays calm and collected about the whole affair. Brimley as usually to his roles has a certain command even in this role as the elderly Ben, and he quietly carries on as really the moral center well. Even as the others fight Ben stands firm in his place caring about what is the important, and Brimley conveys the conviction within Ben as a strong quietly demanding internal strength.
This is a good performance by Wilford Brimley and he stands as the best part of the film, as he not only has the greatest emotional impact with his performance, but as well usually has the greatest presence in the group scenes. I do have to say though watching Cocoon again is that Cocoon is not the greatest of films, and all of the stories seem at least a little undercut in some way. Brimley though does his best to make the most of his parts of the film, giving the strongest performance in the film.