You're right, without being identified as Karthus' home, the Howling Marshes don't really have a purpose. That should tell you that they do more to complicate the lore than enhance it. Moving him to the Shadow Isles fits more thematically.
Conversely, Malzahar, Xerath, Rammus, Amumu, Nasus, and Ezreal all have connections to Shurima Desert.
First, I would like to point out that I'm not trying to outright disagree with you, but I do feel that both lore can be considered valid.
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