Plenty of great points made by the users here, lots of thoughtful responses. I agree that pursuing concepts and themes in these films are important, more so than trying to make everything plausible. I do think that trying to make things realistic hinders story potential, kinda like how after the TDK trilogy fans and people in the business alike took the wrong idea from that trilogy, namely trying to make things realistic and serious which they believe equals "good". And then later studios go back on that and try to pander to the craziness of the properties they own, making things more colorful and outlandish. However, quality still depends on the people genuinely trying to craft a meaningful story. There's a fine difference between making your audience feel engaged and making them feel stupid.
Godzilla films should have the human characters act like actual people with problems and motives, that's the kind of "realism" I expect. Or perhaps the better term is just acting natural and not forced. Think of the scene in Shin where Rando Yaguchi stops to pray when standing in the aftermath of Godzilla's first rampage, that's good stuff right there. Another example is Shindo's scene with the Big G in vs King Ghidorah, a film that while it tackles something as crazy as time travel it still made room for a great scene that felt human. Hell, even Raids Again succeeds in making the human response to the appearance of giant monsters feel impactful in its own way.
Now, this is a crazy genre so having human characters act "zany" in the appropriate narrative is fine. Modern creators in the Godzilla series need to look back on the franchise as a whole rather than just the original or a couple other films so they can see the value of past works and to understand
why this character can be molded to fit different styles. If there is a lesson to be learned, don't go with the mindset of the G98 team which went the route of "we're making an animal, not a monster."
Sometimes kids just want to buy figures of space dragons fighting robot dinosaurs. I still do, dammit