I understand Pariah's point. Cogburn is, in many ways, Wayne's signature role and he made the character his own. Not unlike, say, Eastwood and Dirty Harry.
That being said, I think Bridges could play the character well. It wouldn't be John Wayne's Rooster Cogburn but it could be a lot of fun.
Thats the whole point though isnt it.
Certain roles are very much an extension of the actor, and were who they were because of the actor.
When an actor remakes a film or takes over a role, then they in turn have to make that character their own.
The worst thing Brandon Routh did was try to be Christopher Reeve as Superman, rather than give his own interpretation.
Its one of the things that has always seperated each actor on the Bond movies. None of them has ever tried to play the character the same as the actor before.
Some will bemoan that nobody else should play Cogburn and complain that its nothing like the film they love, but what they are forgetting is, if you remake a film, it shouldnt be identicle, otherwise whats the point of remaking it?