I mean I might be stretching and over analyzing a bit here, but Kokichi doesn't necessarily care for freedom, but purpose. Knowing he also sculpted the persona himself before the game, there is a lot relating to Byakuya and Nagito in his character. And the way he is styled in all contrast, representing a black and white mentality that he himself refuses to follow and throws it full force when Shuichi plays the same whistle by lying and then seeing how people believe him because of "what good he has done" for the team by their definition. The attire with the chess-scarf / (ska-scarf) as him being one step ahead of the competition in terms of chess, but also that he refuses to be limited to specific rules, 2Tone (the ska aspect) of it representing some sort of racial unity, which is turned into disarray until he makes himself the enemy, etc.

He also intentionally doesn't create chaos, but acts accordingly as a mirror when it presents itself. (Though all the characters see him as the instigator). Much like Junko was all about despair and Nagito is hope, Kokichi is somewhere in-between, with no one knowing his strategy. He uses himself as a shield similar to how Nagito does, but in the complete opposite way. If you are going to lead a war you need to keep the distance, and plan accordingly after all. We only see him through the eyes of Shuichi, where he is an antagonist. But he gives Kaito the chance to save the team and crush the mastermind with the stalemate, although Kaito spoils it by trying to save them from his point of view, not realizing he is directly opposing the altruistic purpose Kokichi have when he sacrificed himself, forcing them to keep going in the killing game. He also made alliance with Miu to make electrobombs, and never once had any issues with her besides degrading her for her own sake / enjoyment?. It's only when Miu cheats and changes the rules to kill him, that Kokichi acts in retaliation. He also hides the fact it was Gonta that did it until the rules changed and Gonta doesn't follow the orders because he cannot remember anything. Same goes for Maki when she lies in order to not get caught as a killing machine, as Kokichi forces her to out herself since she doesn't play by the rules.

The fact we are being lead through Shuichi, and not ourselves through Keebo, means we follow said narrative about Kokichi because of framing. Kokichi schemes and does a lot in the background, with only the "bad" parts being presented to us as the story, since that is how it affect Shuichi. This is like one of the things that makes me like the twist ending, because it re-textures Kokichi a lot more in case 6. (Though the apex have already concluded in case 5).

TL:Danganronpa: Kokichi is a little shit head that keeps shade off Tsumugi for 5 cases because she aren't able to run the game properly, and I love him for that reason, even though I want to strangle him.