One thing that comes up for me as I read the oft-repeated expressions of disappointment in the fact that Éowyn lays down her blade and becomes a healer is that it somehow seems upside down. Shouldn't we feel happy for her (or for any character, regardless of gender) who is able to find peace and love and retire from death and slaying? I guess maybe this is the reason why endings to fantasy stories, or I guess any story, are often a little bittersweet, even if they're happy endings. We'd feel the same way if Indiana Jones ever hung up his whip on his study wall, or if Conan ever decided to rule from his throne-room and leave the slaying to his minions. I'm not sure this has anything to do with sexism though, and maybe more to do with what we get out of the adventures and exploits of the characters that we identify with and fantasize about being.
Another thing I wonder about is how many people in Middle-earth are really professional warriors anyway. My sense is, not that many. No doubt Gondor has a standing army given their geography. But elsewhere, it seems that battle is something that is engaged in when it's necessary, not as a matter of course, and being a warrior is just something that you do in addition to whatever else it is that you do. In a world at war, more men take up the warrior role, sure, but what becomes of the warrior when the war is over? The fate of those stuck in the warrior sphere seems lonely and bitter indeed. Not that bitter loneliness doesn't have its attractions.
I'm reminded of the end of John Ford's
The Searchers -- as the rest of the family heads inside the homestead and the camera pulls back through the door, Ethan, the John Wayne character, remains outside, isolated, tragic. He turns and walks away as the door closes. A warrior who is always off to new adventures is also always turning away from home and hearth and family.
Another thought -- the flip side of the expectation that women will stay home and mourn their dead is the expectation that men will take up arms and fight, and die. The social pressure on men to be warriors can be incredible, as Tolkien himself knew full well. So what if you're a sensitive young man, more given to poetry and learning than the martial arts? Well, you take up arms anyway and do your duty, as you can hardly do otherwise without suffering the censure of society. I seem to recall Tolkien saying that Faramir was the character with whom he most closely identified, and I get the sense that it's in this regard too. Faramir doesn't relish his role as warrior, and he can't wait to get back to less violent pursuits when the war is over. Both men and women can be victims of the pressures and expectations exerted by their culture.