So, what is Dark-type's role, really?
The Legendaries and Their Role:
Darkrai is seemingly based off Phobetor, Greek god of nightmares, but its event involving the abandoned hotel seems to imply that Darkrai is actually based off Lovecraft's depiction of Hypnos, Greek god of Dreams. Its design is meant to evoke a ghost, connecting it to ghouls that invade people's dreams that represent sleep paralysis.
Yveltal is based off Hræsvelgr and the unnamed eagle at the top of Yggdrasil. Its cocoon is based off an egg and its patterns are based on arteries, while its fluffy mane gives it a vulture-like look. Its red coloring seems to be based off the red dragon of revelation.
Guzzlord is based on a stomach, but its name means Akujiki King, which means eater Meat Eater King, or Disgusting Things Eater King. Its overall design is reminiscent of a black hole, while itself is a generic kaiju.
The Trainers and Their Roles:
Karen is based off a generic Beauty, particularly those of the original game. She likes Dark-types because of the tough and wild image they portray, and she is known for her overpowering tactics. In other words, she likes Dark-types because they are edgy.
Sidney is based off a generic Biker, who became successful. He likes Dark-types because he uses offensive tactics and he enjoys Dark-types' aesthetic.
Grimsley is based off a generic Gambler(Gamer in localization, PI in localization of DP). He is full of pretension due to being a member of a rich family that was ruined.
Nanu is a former cop who used to be Looker's boss. He currently serves as Ula'ula's Kahuna. He is a completely nonchalant cat person who serves as Acerola's main care taker. He doesn't smile, he smirks. In the UB storyline it is revealed that he left the International Police because he failed to rescue a Faller from Guzzlord.
There aren't a lot of Dark-type legendaries, and those that exist are generally associated with Death in some form or another. There isn't a generic vile or wild beast type of Dark-type. Some Dark-type legendaries are also sometimes characterized as misunderstood, while others are characterized as generically evil.
The Dark-type trainers are rather rare, but they are generally stuck in Elite Four structure. This is because Dark-type often appears as a late-game and mid-game species as well as an early game species. Most Dark-type trainers are focused on the aesthetic of Dark-types, except Nanu, who likes their self-sufficiency. Most Dark-type trainers are also incredibly hedonistic in an acceptable level, and self-confident in a calm but rather self-delusional sense.
Dark-type is not properly covered outside of a generic evil type or morally gray type. They generally appear in Knight in a Sour Armor style or Batman style Dark Knight, a Knight of the Night, that is. This makes them rather popular, but they tend to be rather shallow.