I think you got a misimpression about the fact that the Phial never shone in Orodruin.
The power of the Phial was subdued in Mount Doom. It says so in ROTK. It did not shone because all powers were subdued there, in the heart and core of Sauron's might.
The Phial never shone there. But after the One was destroyed, when Gandalf gave it back to Frodo, it still shone.
Even though the power of Nenya was present in the makiing of the Phial, as well as Nenya, the Phial was not shorn of it's power completely after some time later.
Nenya had no power, as well as Narya and Vilya, when the company went to Valinor. It's last power, to ward off tiredness of this M.E. in favour of their beareres, was lost. And it was impossible now for Galadriel and Elrond to stay here because they longed terribly for Aman.
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"In place of a Dark Lord you will have a Queen! Not dark but beatiful and terrible as the Dawn! Treacherous as the sea! Stronger than the foundations of the Earth! All shall love me and despair!"
--- Galadriel when tempted by the One Ring.
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