I think that the originally planned two films were scheduled to be filmed back to back which makes sense since Shire sets and extras for example would only be needed at the beginning and end. The three films wer decided on so they didn't have to edit much out. So not much extra filming require making the decision potentially very profitable.
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“But Finrod walks with Finarfin his father beneath the trees in Eldamar.”
Christopher Tolkien, Requiescat in pace
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