Well, I’m just talking about balancing the RPS type relationships, which is a delicate (especially while maintaining the metaphors of “Fire” and “Rock,” etc.) but contained and accessible task.
There hasn’t actually been consistent porting options between generations of pokemon, so it’s not as if they’re struggling to reconcile twenty years of legacy schema. They remade the old games partially to deal with this issue. (They applied Abilities to the 'mon in the remakes, so it was easier to trade them forward, right?)
Anyway, they clearly have some concerns about type balancing because they added the Fairy typing in the last generation, specifically to nerf Dragons and maybe to nerf Dark a bit as well.
Also, the Pokemon Company expends a pretty significant amount of resources in hyping up their official tournaments which are highly competitive and have rules designed to keep them competitive (nearly all legendaries are banned, each 'mon must have a unique item, etc.)
Tournaments aside, I think Game Freak probably cares about competitive battling being an overall fun experiences and not feeling “broken” overall. Without Fairies, the only way to take down a pure Dragon type is with an Ice move. Ice 'mon are not resistant to Dragons, though, and they’re overall very frail. So the better option is to pack Ice moves on a bunch of non-ice 'mon. But if you make your whole team Dragon, you still stand a good chance of getting the opportunity of dominating. Blah blah blah. It seems like the saw a legitimate cross-generational balance issue and decided to fix it.
In second generation, I think they basically added Steel, Ice, and Dark because they thought new types were a neat new feature for a sequel. But Dark also served to nerf psychics (in addition to splitting the Special stat).
So yeah: it’s probably not a goal of theirs to have a completely balanced type system, but I think it’s a reasonable priority. Basing the game on an unbalanced RPS system actually creates a chain reaction of balancing issues in other aspects of the battle system, (such as making sure Electric types have limited Physical Attack options, keeping Psychic moves weak, nerfing a particular 'mon, because type alone makes it too formidable). Theses nerfs can feel very tacked-on and artificial–as if they’re fighting uphill against the balancing issue at the root of their system.
Balancing every aspect of the game would be a monumental task to do retroactively, but that’s not what I’m putting forward. Balancing the RPS now would definitely cause some ripple effect that would need to be accounted for. But I think they’d be easily predictable, and the criteria that you need to balance are pretty limited.
Bottom line: of course the game’s going to be unbalanced in every other aspect, and they don’t actually care that much about the type RPS. But it’s perplexing to look at the most basic aspect of their system and think, “Why did you make Scissors weak to Rock and Scissors?”