• "How about we let them fight each other?"
You know, because this is what they DID. They're ancient predators and parasites that preyed upon each other as a part of their natural lifecycle. Plus… you know, and the US and Russia BOTH nuked Godzilla over and over again in the 50's and managed to do… absolutely nothing. The only plan the military has is to hope to take down ALL THREE of them in one go with an even bigger nuke? Right. (Not to mention that Serizawa's family was from Hiroshima during WWII, so the idea of using a nuclear weapon anywhere near a populated city is going to be extremely unacceptable - especially if it doesn't kill them, it's just going to make a bad situation VASTLY worse).
• Godzilla's atomic breath was clearly a last resort, which is why he doesn't use it constantly or until near the end of the battle. It's why he passed out of exhaustion after using it the second time to kill the female MUTO - since unleashing it's a HUGE energy drain (in addition to having a building collapsed on him).
Additionally, the way that they acted like animals but still maintained the old-school kaiju style was really impressive. There're all sorts of little things. The way Godzilla is confused by what the Golden Gate Bridge is and tentatively feels it out. Also when the male MUTO lands on buildings, & when Godzilla tail-slaps him into the skyscraper, they expect them to function like solid structures (like mountains), and are caught off guard when they crumble under relatively small stress. Not to mention, little physical movements like Godzilla fighting by staying in place and physically overpowering them, or the MUTOs focusing on hooking and pulling him off balance, or the ways that the MUTOs interact with each other.
• Godzilla & the MUTOs weren't a threat to humanity as monsters. On the contrary, as monsters, the MUTOs are probably one of the more empathetic entities in the film -- which is really the point. It's the effect of JUST their presence that we can't do anything against, because they're an analogy to our inability to combat natural disasters that we oftentimes contribute to -- hence the Fukushima reactor/ tsunami parallels with (the Janjira Reactor collapsing from the MUTO and Godzilla just approaching Hawaii), 9-11 city destruction (most of the downtown fight), and other large-scale disaster parallels (all the scenes of trying to find lost loved ones) - in addition to the fact that the MUTOs were awakened by strip mining and destroying the environment.
• More to that point, the humans are really just a vessel that follow and give perspective to the helplessness and futility of the human attempts to stop things on their own. Ford & Godzilla's journey also has a small parallel, but that's mostly just during the final battle. For the most part, the humans LITERALLY do not matter At. All. We basically just follow their attempts and the eventual ability for Ford to stop us from making everything worse. We're our own worst enemies in the film, and the scope of everything the humans did from start to finish, doesn't even register in terms of the primary conflict.
Even so, it's clearly not everyone's cup o' tea, and it isn't completely perfect, but it did a hell of a lot right.