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I suppose it depends on what you mean by a "good reason". Conan was going to involve Takagi iirc, but then changed his mind because he didn't want to get him involved and killed. (That's probably reason enough for Conan since he doesn't want to risk someone else's life). Quite sure he said that Takagi was the only one who would act in that instance as well and would need further proof, more than just a random email address to convince the police to make a move. Ai also pretty much convinces him that he shouldn't open "Pandora's box" either, and that the address is too dangerous to be put to use. In any case, doesn't the FBI, or at least Akai probably know the number? Kir and Ethan both knew iirc, although they were CIA, and one of them is deceased It's probably another way for Gosho to stall plot progression.

Yep. That's a clear mistake. (Well even less than clear mistakes count too, but that one is definitely A-grade oversight)