Why she wasn't an archer to start off with I don't know, but now that the League traditionally has one of the Arrows on it anyway, it would be kind of embarrassing for everyone, really. They only have the one thing they do, and giving it to somebody who's already a flying brick and doesn't really need it would be, well, kind of sad. Ollie might as well quit going on missions- what can he do that Diana can't, after all?- and change his name to "Hal-and-Dinah's-boytoy Man."
We could tie it together nicely, though, if Lian Harper wound up as Wonder Girl. She could get powers and a magic bow from Artemis maybe (goddess, not Bana), and get to keep up the family tradition while holding down a good spot on the Titans. (And hang out with Milagro, the Teen Lantern.)