If anything, I'd give Dragons more resistances, to be honest. But they are already plenty powerful they are, so I really have no arguments for the cause other than what I believe. For one, how can Dragons resist Grass but not the similar Bug? And you're telling me they can resist the elements but not a Normal type? I also thought Poison and Fighting resistances might've worked, due to how thick Dragon hide is in mythology.
Dragon's way fine the way it is. Dragon was meant to "resist the elements", similar to the "dragons are impervious to magic" myth from mid-evil times: i.e. Fire, Water, Grass, and Electric. It's weak to Ice, however, because Dragon types are inherently Reptilian/cold-blooded and or because many are fire-breathing. However, Dragon does half to Steel becomes many dragons in myth have been slain by special, mystical swords (although that logic makes more sense if Steel doubled Dragon). Either way, Dragon has no need for a type change, except that I too thought it'd be nice if Dragon did half to Bug, but I think Dark and Psychic should do that.
I never understood some things about the type chart. Like, why isn't Bug weak against Poison? Don't they make poisons specifically for BUGS? Why is Dark WEAK against Bugs? How is darkness weak to a housefly? I don't get that. Why isn't Steel super-effective against a Flying type? Can't you kill birds with a bullet, or are they just pretending? I never understood how Psychics are strong against Poison types, though. That's one of the few that really get my confused.
I think Bug isn't weak against Poison partly because of well...Parasect. That thing is 4* weak to both Flying and Fire as it is. Besides, I think it makes more sense that Poison doubled Water (in the sense of pollution) and definitely Fighting.
Steel doesn't double Flying because Steel's already hugely defensive and doesn't need anymore boosts...If anything, it should either do half or not effect Ghost types. Bullets will kill any living thing (Normal, Fighting, Bug, in this case), except like trees, so it's not too good of a reason.
Dark (and Bug in some cases) is a very conceptual type. When I talked about the type chart years ago to some other pokemon players, based on Dark's advantage over Psychic and Ghost, we came to the conclusion that the Dark type embodies dirty, intelligent, calculated fighting. Psychic and Ghost don't do well because Dark types are mentally very stable therefore cannot be outsmarted or possessed. They prefer calculated fighting (although Dark type MOVES themselves do not follow this description), therefore they are weak against Fighting because Fighting simply overpowers them, and because Fighting embodies "the hero" of the story and Dark embodies "the villain," and we all know the "hero always defeats the villain."
As for Bug, in the case of Fire, Grass, Bug, Fighting, Poison, Rock, Flying, and to Steel, it is very biological in logic. But in it's case towards Dark and Psychic, it seems conceptually based on the "hive-mind" notion. Psychic and Dark can't defeat them mentally or outsmart them because there are simply so much of them and they are so bent on the same goal(s). Balance wise - Psychic and Dark needed weaknesses, and Bug is one of the worst types to exist.
Why Bug does half to Ghost, I can't tell you.