I feel this movie should have leaned more into parody or dark comedy. Because the movie is strongest towards the start when it's spoofing the government bungling that led to the Fukushima Disaster, and using Shocking Imagery from the 2011 Tsunami. I found that pretty compelling and actually laughed about twice because I thought that was pretty clever.
Believe it or not, Shin Godzilla
did all of those things you wished it did. The problem is that satirical comedy is the most difficult to translate across cultural boarders. Did you know that one of the funniest scenes in the whole film was when the PM said "Prepare my suit," and then walked out dressed as a rescue worker? If that didn't strike you as funny, then it was because you were too focused on our own American political comedy of Trump v Hilary to realize the political hilarity ensuing in Japan over the Japanese PM dressing as a rescue worker in real life to reassure the Japanese people that "everything possible was being done to protect their safety." It's funny, but only if you're aware of the subject the film was satirical of in order to "get the reference." Watching these Godzilla movies can often make the foreign viewers feel like Captain America in the Marvel movies, where he doesn't get any of the references or jokes being made until someone mentions "flying monkeys."
Godzilla movies have always been about Japanese politics and social structures. Shin Godzilla is no different. (Fun Fact: Did you know that Japanese audiences cheered in 1954 when Godzilla toppled over the Japanese Parliament building in the original film? Do you even know which building that was without a quick Google search? If not, then it's impossible for you to have an informed opinion about Godzilla and politics and how it can be used to objectively determine the quality of films in the said franchise.) Anno simply took the government debriefing scene from the 1954 film, and turned that
into a modern day satirical movie reacting to the Fukushima disaster. The main issue is that many Americans don't know enough about the events unfolding in the Fukushima disasters in order to get any of the references being made. But, American audiences can certainly jive with the post 9/11 fears expressed in the 2014 Godzilla movie. So regardless of how well a Godzilla movie does what it set out to do, people with certain cultural biases are always going to lean towards the film that references the cultural events with which they're most familiar. In your case, that would be the post 9/11 fears expressed in Godzilla 2014, and that's not a problem at all.
In short, we have our Godzilla movie that has cultural references that we can understand, the Japanese have their own Godzilla movie that has cultural references that they can understand, and no movie is better or poorer for it.
As for character development goes, I'm genuinely shocked that people outside of Japan didn't find Mikako Ichikawa's performance breathtakingly powerful. She is the paragon upon which the entire cast of characters pivots into having healthier discussions with one another and actually moving forward to solving the mystery behind Godzilla's very being. Like, that shouldn't be a thing that is lost across cultural boarders. Those aspects of the film were just universally good storytelling. But, I guess because she didn't have an instantly recognizable "My mom and dad died in a fire" tragic backstory, so I guess it doesn't count as character development to today's "modern" and "sophisticated" audiences.