Kakashi claims that "nothing but emptiness will come of revenge". I agree that the hole in Sasuke's heart can never be filled by revenge. Revenge isn't a way to stop one's hurt, it's only a black hole, always hungry and never satisfied.

That said, I think killing Itachi actually might bring Sasuke a sense of peace and closure, if not happiness. Sasuke smiled after he killed Itachi, seeming relieved ans pleased that at last his purpose is fulfilled and after years of pain, stress, and grief, he could finally rest in the sense that his purpose was at last fulfilled and he could be free from the obligation of killing his older brother. Not sure I'd precisely describe that as "emptiness".

Furthermore, is Kakashi speaking as speculation, or from experience? Kakashi never seemed discontent with the fact that Obito's and Rin's killers were all dead. I'd say that's always been a nice bonus for him. What about Shikamaru? He was happy and satisfied with his revenge.

Fans lord how Kakashi's words are so prophetic and so wise...but how was Sasuke supposed to have a clue about the truth about Itachi's motivations? Normally that kind of revelation doesn't happen; it was a freak twist of fate. There's no way Sasuke could have anticipated that Itachi was acting on the village's orders and had an entirely different motivation for his crimes than Sasuke had originally been told. Had Sasuke never learned the truth about Itachi, I personally think that he would have been satisfied and relieved with at last being able to rest knowing that his parents' murderer and his clan's killer was dead. Sasuke could never fully have peace of mind knowing that his clan's killer was at large.

I don't think Sasuke ever regretted his revenge, not even after his redemption. Sasuke only regretted the route he took to get it, which was unethical and wrong and resulted in him doing some really terrible things and hurting his closest friends. But there is nothing that indicates Sasuke ever regretted killing Danzo. He appeared quite pleased and gleeful that he avenged his clan by killing Danzo, and thereafter he never expressed remorse for killing Danzo. Even as an adult in Boruto, he still appears to dislike Danzo as much as ever as far as I'm aware and personally, I don't think Sasuke ever felt guilty about killing Danzo.

Sasuke's musings that Orochimaru might have had a more justified reason for attacking Konoha than he'd originally thought plus his notable omission of the Third Hokage's death from Orochimaru's list of crimes (even while listing the Kazekage's murder, a person that Sasuke was less likely to care about) implies that Sasuke is pleased Hiruzen is dead and thinks the Third Hokage got what he deserved.

So does revenge only bring emptiness as Kakashi claims? Revenge is bad and unhealthy, especially in Sasuke's case since he allowed his unhealthy obsession with revenge to tear himself apart and ruin his life. So yes, revenge clearly is a destructive and devouring force that will ruin one's life if one isn't careful with controlling it rather than letting it control them.

But I can't help but notice that Team 10 felt pretty good about getting revenge, Kakashi seemed happy with Rin's and Obito's killers being dead (at least he's never shown to be unhappy about it), and Sasuke is pleased that Danzo and Hiruzen are dead.

Sasuke only felt bad for killing his older because he learned the truth which completely reframed the context of Itachi's actions and who was really to blame for the Uchiha massacre. Sasuke only felt remorse for killing his brother because he stopped blaming his brother for the massacre and started blaming Danzo and Hiruzen for it instead. Sasuke still hates Danzo and Hiruzen as much as ever, even in adulthood, and I think he is content (or possibly happy) with them being dead and I don't think it's emptiness Sasuke feels but an actual satisfaction that those men paid for their cruelty.

While Sasuke deeply regretted how he hurt and betrayed his friends, and he hated that he had been wrongly lied to his whole life, I'm not convinced he minded his enemies getting the ending he thought they deserved, and I'm not entirely convinced that Sasuke doesn't derive pleasure from Danzo's and Hiruzen's deaths.

In his current frame of mind during this scene, I don't think Sasuke could tolerate anyone hurting his clan and getting away with it without punishment. I think Sakura hit the nail on the head when she described Itachi as the one tormenting Sasuke all these years, because so long as Itachi was out there, Sasuke could never truly find complete peace until his clan's killer was dead. That, or Sasuke would need to undergo a revelation or a serious shift in priorities. Team 7 was influencing and starting a change in him, but he hadn't actually hit that change point yet. Plus Itachi's interference had slid him back to square one, as Itachi's appearance only served to reinvigorate his single-minded obsession with revenge.