I keep thinking that they are writing her like Eowyn - cold, hard, stubborn - but without any of the more beautiful, loving qualities that make Eowyn so compelling.
On reflection, I think Eowyn is a harsher character than ROP Galadriel. Galadriel knows who she needs to fight and why. Eowyn wants to win battlefield glory, and the field just happens to be Pelennor. She is angry at being forced into the "softer", more traditionally feminine, role of caring for her uncle, and even Gandalf agrees she has a point.
Even her crush of Aragorn takes form of the desire to fight at his side.
She does get her character growth after Pelennor, which would probably be two seasons after her introduction, if LotR was filmed as a streaming show.
ROP Galadriel reminds me, not of Eowyn, but of iconic male heroes like James T. Kirk, who always know best, do whatever they want without regard for authority, and of course turn out to be right all along. Except Galadriel is beginning to learn diplomacy only 4 episodes in.