someone please explain the logic behind why she had to volunteer herself to be a slave with a bomb around her neck to an organization that doesn't view you as a human, and instead as a leash for your partner.
The organization likely isn't too interested in "risk factors" like her or other possessed going around freely; instead they may avoid execution by being useful to the organization, like being a demon bait as was mentioned (and shown) earlier on.
In her case it also allows the organization to gain leverage over Kuro, who, as we can gather from Benio's (the cadre lady) internal monologue here, is otherwise not too well under their control.
As for why it "has to be this way", for our couple here, it's either this or whatever constant fight they would have to wage, had they refused to co-operate with the organization, so not a lot of good options available. For the organization, it's just politics and power dynamics - this whole shtick of "bending the rules a bit" for the carded individuals is definitely more about "usable pawns" than any sort of compassion or mercy on their part after all