I always felt Karkaroff was way more pivotal than people give him credit for. His leadership at Durmstrang isn't just about showing up for the Triwizard Tournament. He's this walking embodiment of a former Death Eater who's made a specific, self-serving deal for survival. That choice ripples out. By bringing Viktor Krum to Hogwarts, he inadvertently puts a powerful piece on the board that Voldemort's side can't directly control, but that Dumbledore can leverage through Hermione. More crucially, his frantic attempts to avoid the Dark Mark's return, like running to Snape, expose the growing fracture among Voldemort's former followers. His fear is a barometer. It shows that the power dynamic isn't just 'good vs. evil' but a messy scramble among the guilty who want out, which Snape ultimately masters and Karkaroff fails at. His eventual fate—trying to run and being killed—cements the new rule: there's no neutrality anymore. Dumbledore's side or Voldemort's side. His failed leadership, rooted in cowardice and bargain-hunting, helps define the stakes for every other adult character with a shady past.
Plus, from a pure story mechanics angle, his presence at Hogwarts heightens the tension around Moody/Crouch Jr. He's a red herring. Readers and Harry are meant to suspect him of the dark deeds, which perfectly masks the real threat hiding in plain sight. Without Karkaroff’s shifty, untrustworthy vibe taking up so much suspicion oxygen, Barty Crouch's plot would have been a lot harder to pull off.