Question: If Blofeld wanted to eliminate Tiffany Case, then why didn't he kill her when he kidnaps her later on the film, instead keeping her alive and unharmed on his oil rig in Baha? In fact, he doesn't consider harming her in any way until he notices that she's helping Bond (with swapping the tapes round) on the rig.
Answer: It could be any number of reasons. For one, Tiffany's young and beautiful, and he may have been attracted to her. Some men, even evil ones, balk at killing a woman. She might also be more useful alive, at least for the short-term, to be used as a hostage or a bargaining chip or for information. He may also have intended to recruit her to his side.
Answer: He didn't kill her because she seduced him into believing she was sexually attracted to him, his power and wealth.
Question: Is it actually explained in the movie why Willard Whyte is in hiding?
Answer: If you mean by hiding - why is he never seen normally - then it's because he is a recluse and doesn't like to be seen in public (like Howard Hughes was). If you mean by hiding - why was he not seen during the movie - then it's because he was being held captive by Blofeld and his minions. Spectre didn't want him out and about ruining their plans.
Chosen answer: Blofeld and Spectre has enough diamonds for the laser he is building to hold the Earth hostage. In typical Spectre fashion, since he is finished with the operation, he wants to leave no loose ends that could tie Spectre into the mix.
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