What you write is logical, but if a mother has anything more important than her son, there is a problem,We don't have all the information, but the reality from what we can tell so far is that the gambit is a possible solution to a problem that IS far more important than Kane's life.
Humanity is legitimately on the brink of extinction. If the Karlssons and the DeKocks work together, then with some luck they might actually be able to fix the planet. Callista isn't sure exactly how things will play out and might have some backup plans but she seems to be placing the bulk of her chips on her son being able to unite the two families.
Survival for Kane was never going to be easy no matter what. The gambit is the best way to save Kane AND the best way to save humanity. As for Kane going into stasis like Astrid, what good does that do if there's no one alive to even figure out a cure to the disease lol.
because what's the point of saving humanity if in the meantime your son dies or becomes a degenerate servant, someone else's toy.