People over at Tohokingdom have been arguing that Shin is very far removed from the origins of Gojira, but when I think about it, new nuclear powers aside, Shin Gojira, in his final form, is pretty much exactly like the '84, so if you think Shin doesn't embody Godzilla, neither does '84.
In Gojira, Godzilla is a rising threat that starts with sinking ships, then makes makes multiple landfalls that progressively grow in destruction, his final being full of unleashing flame and destruction upon Tokyo.
In '84, Godzilla is once again a slow rising threat, first attacking a sub, then making landfall and destroying a nuke plant, finally making full landfall, but, when he does, the majority of his destruction happens while he's being provoked. Military attacks him at sea, lots of flame and destruction. From there, he's just strolling through the land, with some destruction by nature of his size and surroundings, and he attacks a train only when it hits him, then back to strolling around until the military lures him for the test and then Super X comes in and that's the point at which a good chunk of the city is destroyed.
In Shin Gojira, Godzilla is back to a slow rising threat, first a sea creature that caves in a tunnel, then he makes his way into a river causing tsunami level waves flooding and destroying things, then he emerges from the water and destroys mainly due to being an animal trying to survive in a new environment, not maliciously, and when he finally lands in his main form, he's just walking along with things crumbling in his wake or when provoked by the military.
I don't think '84 or Shin lost the idea of being Godzilla, other than taking the purpose/intent out of his actions. In Gojira, he walks around and stops to purposely shoot fire at buildings or smash them. A trait which carried through most of the franchise, but I don't think is the make or break trait of being a faithful depiction of Godzilla.
