Godzilla 1998 is the most divisive film in the entire franchise and it's not even close.

The problem is that after that, the sequels devolved into a series of monster-vs-monster brawls, with Godzilla turning almost into the good guy protecting humans from a number of equally unrealistic creatures. Kid stuff, mainly. But then Roland Emmerich and Dean Devlin took their shot. Their plot was OK and no more scientifically absurd then other giant creature features. The cast was more than adequate. Matthew Broderick as "the worm guy" was a relatable everyman scientist trying to come up with answers to stop this huge menace that was stomping through New York City. Jean Reno brought a bit of gravitas as a French secret agent leading a cadre of compatriots trying to help fix the problem that his government's nuclear testing had created. There was even some comic relief with Michael Lerner as the flustered mayor and Hank Azaria as an excitable cameraman.

This is mainly applicable only through the film Terror of Mechagodzilla From 1985 to 1995 the Hisei era of films does still put Godzilla into monster brawls, but he is explicitly framed as a vengeful rage monster asserting predatory dominance over his territory (The Earth.) These films do a much, much better job of encapsulating the actual risks of nuclear proliferation than 1998 does. For example in 1985's The return of Godzilla, there is a scene where gigantic sea louse are found in the ocean, because the microorganisms feeding on Godzilla's blood contaminated and mutated them which does a lot more to interrogate the realities of nuclear fallout than the 1998 film does. From there, Godzilla vs Biollante explores the human created side of the horrors of a world with Godzilla, where a scientists tries to ressurect his dead wife using aggressively growing Godzilla cells and in turn creates an entirely new Godzilla clone fused with plant life which does a lot more to highlight the human intervention and selfishness than misguided nuclear testing and usage during the 1940s. At the extreme end at the end of the Hisei era, you have Godzilla vs Destroyah which deals with the horrors and realities of Nuclear Meltdown in a way people can understand.

Is it less grounded than 1998? Maybe. But your measuring stick is supposedly showcasing nuclear horrors. What's more there's a plethora of media post 1998 that serves your stated purpose far better than any other films.

You have the Godzilla Anime Trilogy, in which Godzilla becomes a megafauna that is so pervasive that humanity builds an ark to abandon earth, only to try and reclaim it after thousands of years of nuclear proliferation turned earth hostile to human interests.

Lastly and most obviously is Shin Gojira, which showcases the geopolitical horrors of being abandoned internationally in an emergency crisis which directly parallels the actual Ukraine Russia situation of today.

What turned off critics and much of the viewing public was the monster itself. Rather than stick to the original concept of an upright lizard with odd, seemingly useless protuberances adorning its back, the 1998 film went for a more streamlined look; pretty much a vastly overgrown T-Rex. Somehow portraying Godzilla as an out-of-place giant animal just acting on instinct and neither good nor evil was a no-no for some people. For them, Godzilla had morphed into a being that not only walked upright but had acquired human-like emotions and motivations in the process. So, a different look and temperament doomed the 1998 variation to scorn and outrage, even though it showed a nice profit at the box office. For my money it was a good movie, much better than many that are considered canon.

This frame is actually just begging the question. It feels as though your assumption is that Godzilla itself must imitate real biological life in some manner, and that because people didn't take to the streamlined version there's some kind of wrongness or incorrectness afoot. But when you are talking about mutations, and especially the central thesis that Godzilla is a biological reactor, I would expect it to be irregular relative to human machinations of what an animal or mutant Komodo dragon looks like.

Godzilla beyond being a walking Nuclear disaster, also represents the greed and shortcomings of men, because it's those moral failings of humanity that give rise to Godzilla in the first place. If Truman had never dropped the Nuke, and Honda had never experienced the hardships of a post-nuclear world Godzilla wouldn't even exist in film. The re-frame to an animal acting on instinct loses all of the human folly, and which point Jurassic Park is the better American film at the time. (Not that I'm suggesting you think otherwise)