Aside from Tolkien's far greater skill, the main reason why Galadriel and Eowyn work and so many others fail is that G & E are both presented as exceptional.
Galadriel is second only to Elrond as the most dominating person among the free people's of Earth; and she even has a kind of priority over Elrond in being older, having been born in Valinor - and therefore having the greatest personal 'magical' power (and from being his mother-in-law!).
However, Galadriel is presented as exceptional. Within the Lord of the Rings this exceptional nature is implied by her being the only women of the White Council, and among a handful of the most beautiful women of all time. Further, in the Unfinished Tales and Silmarillion it is emphasised that she was even more exceptional; in being a woman of 'Amazonian' stature and strength - similar in combat ability to all but the very greatest elf warriors.
But Tolkien never asserts that this makes Galadriel typical of 'women' - on the contrary she is an unique phenomenon, and marked out as such from birth. She is the female complement to Feanor - both High Elves who attained god-like stature due to their attributes.
By contrast, modern authors generally imply or actually assert that exceptional women such as Galadriel are numerous - either in actuality or in potential; or would be numerous, if not oppressed; or should be normal if women were properly motivated - by which they mean pursuing success in the public realm rather than in the family context.
Galadriel is indeed married to Celeborn, and had a daughter. This merits analysis. Celeborn is officially the ruler of Lothlorien (one of only two large elf kingdoms, the other being Mirkwood) - and described (in LotR) as the greatest of the elves of middle earth; because he is a Sindarin elf, born in middle earth - but as such of lesser wisdom and authority than the High Elves. He is a member of the White Council, along with other Sindar such as Thranduil of Mirkwood* (who he outranks in age and experience, and because of his wife), and Cirdan the shipwright - but while Galadriel defers to Celeborn in public, she is clearly a personage of greater stature than her husband.
Anyway, Galadriel is married and a mother - and the greatest female power in history; and there is no other like her among the Children of Illuvatar.
What about Eowyn? She is a warrior, who does the great feat of slaying the Nazgul's flying beast; then (after Merry has made her sword effectual) the Witch King and Chief of the Nine; one of the greatest heroic feats in the entire history of Middle Earth. Clearly, an exceptional woman - and she is an ordinary mortal Man, and her success is in the realm of pure fighting, which is a masculine domain.
However, it is neither implied nor claimed that Eowyn is the match of the male Riders of Rohan in strength or swordcraft - as she could not have been; and her great feat was not the product of her being a great warrior, but the product of amazing courage fortified by her love for Theoden; a feat perfomed to protect her uncle and adoptive father.
Courage, yes indeed; but also a desperate, reck-less disregard of her own life. Because - like many and probably most real-life exceptional women, women of genius - Eowyn is (until she loves Faramir) somewhat crazy. So she is Not presented as a 'role model' or template for how 'women in general' ought-to live - indeed when healed in body and spirit; Eowyn quite explicitly abandons her life as shield maiden, and man-in-disguise.
So, what can we learn? In Tolkien as in real life, there are exceptional women of high attainment in the public realm - and also that such women are exceptional, they are rare. Furthermore, when they are mortal Men (not semi-divine elves), such women are often somewhat crazy, extremely odd - and recognised as such.
So there are real warrior queens, like the English national heroine Boudica (Boadicea); and like Boudica they are often damaged, crazed persons. There are also rare and exceptional women who are truly great political leaders - like Queen Elizabeth I - but she was also an extremely strange person, and by no means a model for women-in-general.
There are many women genuises, especially in literature; but again they are rare and (almost always) somewhat crazy, in one way or another.
(Don't take my word; try for yourself - First make a list of the best-ever women literary authors - novelists, essayists and poets (there aren't any great women playwrights); and then evaluate them biographically for craziness, chaos, weirdness, extreme eccentricity etc.)
So Tolkien's ability to include powerful and exceptional women who accomplish greatly in traditional realms of masculine attainment - and to do so absolutely convincingly in narrative terms; is simply that Tolkien knows such women exist, but he never tries to pretend that they are anything but exceptional.
Tolkien does not try to pretend that such women ever have been, are, could be, or should be, anything other than very uncommon.
*Note added 5 August 2023: On further consideration, Thranduil seems Not to have been a member of the White Council; because in The Hobbit the King of the Wood Elves of Mirkwood (i.e. Thranduil) did not participate in the deliberations and actions of the White Council is forcing the Necromancer (i.e. Sauron) from his stronghold in Mirkwood (i.e. Dol Guldur).




