The World Government has always had a problem with Nico Robin and the knowledge and abilities she holds. She knows probably more about the history of the world than pretty much anyone. She can read the Poneglyphs, and might be the lone survivor of Ohara.
Her bounty poster says wanted dead or alive. Her falling into someone’s hands is the worst possible thing. If Big Mom or Kaido gets her, it will be a terrible thing.
I doubt the World Government knew her involvement with the Revolution army because that could potentially have led to another war. But they caught her “twice” in the story and had no intention of killing her.
The first time was at Enies Lobby, they successfully captured her, but they did not really attempt to kill her. The second time is post time-skip where they captured the fake one, and now they are trying to capture her again.
This time stood out though. They were told to capture her alive saying she is a target for all pirates. Why not just kill her? That has to be a lot easier.
From World Government perspective, if Kaido goes down then that opens up the road to Laugh Tale and the One Piece. If you control Robin you can find out what she knows and maybe even beat Luffy to the One Piece and destroy it. No One Piece, no Pirate King, no risk of being overthrown. What are your thoughts?