Two explanations I've heard for that Rob is that 1) the eagles are a polity of their own and might have other concerns, or been restricted in their actions by the Valar as, IIRC, the eagles are maiar, or 2) Sauron would deploy his own fliers against this rather obvious ploy, which would risk giving him his damn Ring back.
Because, well, I doubt Doug would leave it there.
Because, well, I doubt Doug would leave it there.