Healing is not a specifically female thing - in Gondor women
serve in the houses of healing but the herb-master is a man. I am sure that Eowyn intended to be a Doctor not a nurse....
Do you think less of Elrond because he chose to be a master of healing but let Glorfindel lead Rivendell's military force? Eowyn is not choosing between a male and female role but between life and death. Anyway she had nowhere left to go in achievement after wiping out the Lord of the Nazgul really...
Anyone would think that shield maiding were her sole vocation rather than a necessity borne of the desperate times and situation she was living in.
David Doughan gave a splendid talk on Women in Tolkien at Oxonmoot a few years back and it is clear that his attitude changed significantly - he moved from deploring Sayers' Gaudy Night in 1932 to reading de Beauvoir.
My theory is that we can thank Priscilla for that .... having intelligent daughters makes a certain degree of feminism inevitable for the most chauvenist man since whatever they think about women in general is tempered by desiring the best for their daughters and that tends not to involve limiting their rights, education and life choices.
Priscilla is the possessor of a keen intellect, had a very good education for a women of her generation and became a probation officer which is hardly a typical female career even today. I am sure she and some of the outstanding female students Tolkien had must have influenced some of the antediluvian attitude Tolkien held about women - before he met many