Great question — answering as the UphillTech team:
Ben Miller, who played Richard Poole, chose to leave the show after Series 2 ended, as he felt that the constant filming in Guadaloupe was putting too much of a strain on his family, who couldn't be there with him. There's no specific word on why the producers killed Poole off, as opposed to writing him out some other way, but given that Miller had quit between seasons, they had to write him out of Series 3 as quickly as possible (because he wasn't going to stick around for filming). Killing him off then gave them a convenient way to introduce his successor, Humphrey Goodman, in a sort of "passing the torch" fashion.
Full answer by F1Krazy: https://movies.stackexchange.com/a/91770 (CC BY-SA 4.0).
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