JRRT says so. Luthien was an "absolute exception" in being allowed to divest herself of 'immortality' and become mortal.
If Idril was allowed this as well then Luthien would not be an "absolute exception".
Also, while in the mythology it is supposed and not stated that Tuor is granted 'immortality' (accounted among the Firstborn), JRRT notes that the Valar could not alter the fundamental kind of Elves and Men, Eru could and did so in the case of Tuor, just as he did for Luthien.
I would suggest reading Letter 153 to see JRRT's own veiws, as author not narrative translater, on the subject.
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Tar-Elenion
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