Ahaha, Ioreth/Éowyn. Personally, I don’t think she’s a coward at all (suicidally depressed, rather), but … actually, she’s a LOT like Boromir, IMO. Her glory and Rohan’s glory are pretty tightly intertwined.
She doesn’t come across as…
Actually, it was a really common interpretation when I was in the fandom. I can’t remember if Éowyn was relieved of command or not at Edoras (I don’t think so, but I recently heard someone arguing that she was? idk). However, I think her motivations are pretty clear. (Quoting mostly just because I love the quotes, ha.)
'Shall I always be chosen?' she said bitterly. 'Shall I always be left behind when the Riders depart, to mind the house while they win renown, and find food and beds when they return?'
'A time may come soon,' said he, 'when none will return. Then there will be need of valour without renown, for none shall remember the deeds that are done in the last defence of your homes. Yet the deeds will not be less valiant because they are unpraised.'
And she answered: ‘All your words are but to say: you are a woman, and your part is in the house. But when the men have died in battle and honour, you have leave to be burned in the house, for the men will need it no more.’
'What do you fear, lady?' he asked.
'A cage,' she said. 'To stay behind bars, until use and old age accept them, and all chance of doing great deeds is gone beyond recall or desire.'
For into Merry’s mind flashed the memory of the face that he saw at the riding from Dunharrow: the face of one that goes seeking death, having no hope.
'My friend,' said Gandalf, 'you had horses, and deeds of arms, and the free fields; but she, born int he body of a maid, had a spirit and courage at least the match of yours. Yet she was doomed to wait upon an old man, whom she loved as a father, and watch him falling into a mean dishonoured dotage; and her part seemed to her more ignoble than that of the staff he leaned on.
’[…] My lord, if your sister’s love for you, and her will still bent to her duty, had not restrained her lips, you might have heard even such things as these escape them. But who knows what she spoke to the darkness, alone, in the bitter watches of the night, when all her life seemed shrinking, and the walls of her bower closing in about her, a hutch to trammel some wild thing in?’
'And it is not always good to be healed in body. Nor is it always evil to die in battle, even in bitter pain. Were I permitted, in this dark hour I would choose the latter.'
'But I cannot lie in sloth, idle, caged. I looked for death in battle. But I have not died, and battle still goes on.'
'I wish to ride to war like my brother Éomer, or better like Théoden the king, for he died and has both honour and peace.'