Tolkien loathed allegory. It was too obvious; too blatant; too literal; too dead. In allegory one thing means one thing and that’s it. Myth, on the other hand, is alive. It’s a real story with the real ambiguity and complexity of real life. Tolkien’s world is multi-layered and yet full of Christian meaning all the same.
In LOTR one female doesn’t represent the Blessed Virgin Mary; they all do. Galadriel and Arwen and Aragorn’s mother all represent the Blessed Virgin in different ways–so does Rosie back in the Shire for that matter.
At that moment the Christian story comes alive again, Our Lady Eowyn reveals Our Lady Mary who also, with her meek victory and humble strength reclaims the battle as the second Eve and tramples the serpent’s head.