Why? I think that Godzilla vs Hedorah is one of the most authentic Godzilla movies. One of main ideas of the series was consequences of humans' mindless and careless treatment of environment. In fact, most of giant monsters in the series were just a metaphor of direful disasters that will befall the humankind if they continue to treat the world around them in the same way (nuclear weapon, pollution, genetic experiments, etc.). In this sense Hedorah, the result of careless pollution of environment, is a monster completely fitting into the spirit of the series
That's the problem, the movie pulled a "Captain Planet."
If that movie didn't make "sense" to you, then I have no idea what you understand as "sense" of the series. IMO, if there are movies that indeed didn't make any sense, those are the few last movies, Final Wars among others, that were centered completely around mindless fights of monsters against each other and fancy CG effects.
Funny enough, I like Final Wars. That was awesome. It has monsters fighting and humans fighting, what more do you need? Yeah, a plot but it had that. It's just fun. That and I got kick seeing Godzilla waste Zilla.
As to the whole flying Godzilla scene from the same movie, well, if you think it was cheesy, you could say the the whole premise of the series about a giant dinosaur with atomic breath is cheesy from beginning to the end. Bashing Godzilla flying through his atomic breath makes as much sense as bashing sugar for it being sweet. *shrugs*
Godzilla never was a "realistic" monster and that's what makes the series unique. If you want completely realistic giant dinosaurs, watch the USA Godzilla movie or Jurassic Park.
Here's the thing, when Gamera flies, it's in character of him. With Godzilla flying, it's way out of character.