Carbink's attack stats are pretty bad, so it wouldn't be my first choice for a playthrough. However, against the League, its STAB moves can hit Kahili's entire team super effectively, along with two of Acerola's Pokemon and and a good chunk of of Hau's team. There are better Rock and Fairy types you can use, so I really wouldn't recommend Carbink for in-game play. But of course it can still work.
As a Pokemon designated to catch other Pokemon, Carbink isn;t amazing, as you have options like Absol that work better. It has a niche with Skill Swap if you're trying to catch something with an annoying Ability, but it doesn't learn classic catching staples like False Swipe or Thunder Wave. There's really no reason to use Carbink as a catcher unless you really need an Ability suppressed.
Bear in mind I don't know a lot about Gen 7 competitive, but I could see this thing as a Screen Setter in lower tiers, with access to both Light Screen and Reflect. Give it a Light Clay to prolong the Screens, and your teammates can put in work. It learns Hail, Sandstorm, and Sunny Day, so it could be a really bad weather setter. It can also set up Stealth Rock and Trick Room for more support options, but it's pretty outclassed by other Pokemon with those niches.
In conclusion, Carbink isn't a very good Pokemon at, well, anything. It can work, but not as well as other Pokemon.
Hope I helped, and congrats on the shiny!
