Thing is, its rather difficult to characterise what is essentially an animal, albeit one that leaves a footprint larger than most houses.
Actually at this stage now, they're not even animals anymore, they're forces of nature. Even in the Toho films, Godzilla isn't really treated as a hero in the traditional sense, but more as something dealing with invaders in its territory. And in the Toho films, no matter how much Humanity tries to combat Godzilla or other Kaiju, its all for nought, much like our attempts to combat the hurricane or the storm.
Something you never see in the Japanese films is the aftermath. You don't see memorial walls, or the walls covered in pictures of missing loved ones. You don't see the reconstruction, the rebuilding of cities and lives. You see the devastation, but you don't see the cost. Its just "BAM!", Godzilla just killed a cyborg chicken from space, but by the time the next film rolls around, every city is intact waiting for the next round.
I actually enjoy the fact that the Legendary films show the human cost. People are terrified, scared of potential kaiju attacks. The films revolve around Godzilla and the other kaiju, much like disaster films revolve around the disaster in question.