Since the Succession is over and no more war-time, I think there is an dress-code issue here. Like Queen supposed to wear a crown in peace time, but in war zone it would be very foolish and dangerous. The same for the Captain-General. She supposed to wear a specific uniform, which includes a sword. But come the war-times again, I'm sure we'll see her using bow and not a sword.

The quote from WH is kind of misleading. At the time, there was a lot of threats to Elayne's life and Birgitte didn't have time to play with swords. Now, however, it's perfectly OK to show the sword on her hips, since it's not bothering her.