Also consider why Blackbeard captured Pudding to begin with. He refers to her as the three eyed girl, meaning that's what he values in her. The reason Teach took Pudding is so that she could use her third eye to decipher the road Poneglyphs, but Pudding will in no way help Blackbeard get what he wants, not willingly, meaning he'll need to force her to do so and the only way that would be possible is through mental manipulation. Laffitte can hypnotize Pudding and force her to decipher the Poneglyphs. Pudding is a prisoner who must be mentally manipulated to play her role for Blackbeard, Laffitte makes the most sense as the one tasked with overseeing that plan.