"Character actor"
They say he's a "character actor" versus a "leading man." When I think of a character actor, I think of a guy who's a bit less than conventionally handsome - Steve Buscemi, Willem Dafoe (depending on the lighting), Kurt Russell, or the late Philip Seymour Hoffman.
I think Kevin is very handsome, and he was downright pretty in his 30s and 40s. He has a lovely smile and actually nice facial features and pretty lips. I like his voice also.
He's played the lover/husband in many movies - so, while I understand he is an extremely capable and nuanced actor - perhaps one of our top actors these days? - why is he seen as a character actor almost exclusively?