OK,
lots of what-ifs here, but,
Suppose Elfhelm knew that Dernhelm was Eowyn. Why allow her to go? This might bring us back to the original question!
For some reason I've always though of Elfhelm as a youngish chap, 20s-30s anyway, no idea why!
Anyway. Imagine that Elfhelm was a friend of Eowyn (even just possibly rather liked her in a romantic way!), and of course the top nobles would all know one-another pretty well. Why be sympathetic to Eowyn's wish to ride to battle? He probably wasn't aware of her deathwish. Perhaps this gives us some insight into Rohirric gender roles with respect to warfare.
Did Elfhelm feel that it was Eowyn's 'right' to go into battle as a shieldmaiden, should she choose to do so? I could certainly imagine a friend of Eomer doing the same for him if he had been 'left on the bench'.
Perhaps this was based on some old saga or song or something that provided legendary precedent, or a real incident from Rohan's past? Maybe Elfhelm had lost hope too and thought it was more glorious for Eowyn to go down fighting in a hopeless battle than wait for Rohan to be over-run?
Eomer I think later denies that any other women of Rohan have ridden to battle, but did he personally check all 6000 'men'? - He'd have got some funny looks!
