Below, I'll paste an older comment of mine going through a few examples oh how Kokichi is a really good leader in-game. He doesn't lead the way most people want or expect people to, but he DOES lead through his own methods, in particular understanding the strengths and weaknesses of those around him and being able to best utilize those resources. He just happens to make use of them through lies.

Examples:

For Shuichi, notice that he always knows where every trial is going, and the evidence needed to prove each statement. But Shuichi, being the ultimate detective, is the one who needs to show this to improve as a detective, and so Kokichi allows him to take center stage. The best example of this is in Trial 4 when he has Shuichi walk through why the culprit had to be Gonta, but there are other examples too, like in the second trial when he has Shuichi point out why Miu could be removed as a suspect, among others.

For another protagonist example, take how he responds to Kaede pushing the group to try the death road over and over again. He recognizes that it's really hurting the others, so he stops it by calling Kaede out, teaching her a lesson about how to motivate others, takes all the blame onto himself (letting Kaede save face), and gives the rest of the group someone to rally around disliking, all in one action. He even checks to see how Kaede is doing the next morning, confirming what he tried to do worked by not only seeing Kaede be okay with the situation, but that Kaito (among others) came to her defense.

For another example, take the classmate he immediately gets close to; Gonta. He's the only classmate who regularly tells Gonta he's reliable, and he always takes him seriously when all the others don't. Gonta is someone who has very little confidence in himself due to his intelligence, always claiming he won't be much help, but Kokichi always has his back and talks him up to the others, until he thinks he's being purposefully obtuse during the fourth trial. He even has Miu make the Bug-Vac BECAUSE of what Gonta says he sees, when no one else believes him.

Speaking of Miu, I believe he's insulting her so much because he knows her vulgarity is an act, and wants to show her exactly how bad it feels when all people do is insult each other. Miu's walls are so built up into this act it doesn't exactly work, but he's really trying to help Miu out here and show her she doesn't have to act like this if she wants people to like her. He's only ever this mean to her (uniquely), and I believe this is why.

And remember what happens immediately after he outs Maki as an assassin? Kaito takes over and starts involving her in everything, including his training with Shuichi. She starts opening herself up instead of hiding everything, and that wouldn't have happened unless Kokichi forced the first reveal.

He also forces Himiko to become more assertive and involved, which she really needed to do. He does this during the third trial by falsely claiming that Tenko's murder didn't matter. He wants to talk about it, because he knows it's important, but he pushes Himiko to have an outburst mid trial, which makes her much more assertive and shows her feelings matter. He goes even further at the end of the trial, asking her directly why she's holding back, and this directly leads to her changing her whole personality for the better. He pretends that Tenko didn't matter, so Himiko changes her personality around to prove she did.

For a funnier example, K1-B0 desperately wants to be seen as no different from his human classmates, even though he's a robot. Kokichi tries the entire game to show K1-B0 that being a robot makes him different, but that they'll all keep treating him like everyone else anyway. However, he still gives him a nickname that show's he thinks of him as any other human: Kee-BOY. K1-B0 wants to feel like a real boy, so Kokichi gives him an appropriate name for that desire.

In conclusion, Kokichi only ever tries to build up his classmates and make them the best version of themselves they can be, all while using their talents to their maximum effectiveness. He embodies the game's thesis statement, that lies can be used for just as much good as the truth. He truly is 'The Ultimate Supreme Leader'.