It appears you never made it to the third volume Peter.

I read somewhere that Tolkien used to read bits of the work in progress to his children, and Eowyn was to some extent his response to his daughter's complaining that the women didn't get to do much.

Books are an expression of the experience of the people who write them. For Tolkien the key experience was probably the Western Front. There weren't any women fighting in the trenches. There were women in the war, but in the field hospitals and so forth. That's reflected in the way things happen in the Lord of the Rings.