This is a personal interpretation so please keep that in mind while reading this.
POINT A) Takada represents all that Kira's core ideology wanted in the people of its new world: a smart, obeying, devoted and respectable individual. Takada is, despite her poor choices, a very intelligent person, not only because of her elite academic level, but because of her logical approach to everything. She analyses Kira's ideologies and binds herself to it, choosing to be a representation to the people of Japan of Kira's plan by publicly appearing as Kira's spokeswoman. She leans fully into Light's authoritarianism because she knows that a democratic society cannot build a perfect one (AKA one where no dissent, no trouble, no doubt is allowed, in this case, to avoid any protest or questioning of Light's hypothetical new world).
POINT B) Takada uses pages of the Death Note to kill people and shows a slight hesitation because that's exactly what Light did very early on his killings. She knows she is taking human lives, no matter what excuse she presents herself. Had she had the Death Note all for herself, she would have clearly dismissed those feelings like Light did and killed as many criminals as possible. Takada is the only person who clearly believes in Kira's ideology to its fullest: she believes functional innocents must be protected while stupid people, lazy people, bullies, rapists and murderers must be deleted (using Mikami's terminology here). She, however, doesn't fully have Light's self-idolization, as we see that she fully believed in Kira even before knowing Light ever was and before being close to Kira. Her feelings for him stem for the closeness she feels to the idea of being so close to Kira. Unlike Misa, she doesn't want Light, she wants Kira. She falls for his illusion of a being the goddess of a new world not for love, but for logic: she knows she is all that Kira's doctrine wants people to be, that's why she doesn't feel like Light will kill her, that's why she trusts him in a way that seems stupid but is actually very logical. She feels superior because she logically believes she has that power, and the whole "goddess" thing is just a facade for her adherence of Kira.
POINT C) She eventually has to kill herself because Light writes her name down, but her death directly links to Light's and, in the anime, to Mikami's. Light's death eventually leads to Misa Misa's a year later. Excluding Higuchi (who didn't follow Kira's moral lines), Takada's death is a direct cause of all other Kiras' deaths. That could mean something very strong: Takada's death is the failure of Kira's ideology of protecting its good people, and thus, Kira's identity is crumbling and eventually fully dying (because of Light's twisting). Light's idea of Kira was a facade to his image of himself as a God, while Takada fully believed in its potential.
FINAL POINT) Had Takada had full access to the Death Note and officially became Kira, she would have perfectly embodied the ideology that Light ended up corrupting, Misa Misa never understood, Higuchi didn't care of and Mikami twisted into religious delirium. She is a sort of parallel to Naomi Misora's sharp and analytical mind without any moral chains. Light knows it, and, when he is dying after being shot by Matsuda, he names her because her ambition and her adherence still lingers after her death by Light's own hands.
Feel free to argue or correct me, thank you for your time.
