Let him call, because again, Agasa was the one who set up this secret, he should be the one defending it. Again, the parent shows up out of the blue here, but I kinda wish they didn't. Because Shinichi's the protagonist, he has to deal with everything in the end, but I want Agasa to be confronted. Have him make up more lies. Bring in the parents slower, have them contact Kogoro to arrange for Conan to stay long term and work out payment. Ran asks about the parents and Kogoro is like 'oh it's fine, they're covering his stay', and Conan's going '...? ???????'. Agasa denies having anything to do with it on Yuusaku's orders. Conan frets about it for a while and they actually see how he'd react to potential unknown danger. And then spring the 'kidnap him' trap to fully show him what could possibly happen.
But I guess just 'kidnap him and potentially give him a heart attack to prove that death is a real possibility' without any setup or warning is fine, too, sure.
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