I think it would've been a cool route to go down to have Clara know a few things about the Doctor. Because for the first time in ages here's a companion that doesn't really trust him or know what to make of him and she's very guarded (and can we blame her?). Knowing a few of his secrets could've helped establish that trust and made for a nice interplay between them as time goes on. But I guess the writers have reserved that for an annoying character I wish would just go away instead.
Who knows...maybe when Moffat finally shows his hand with where the whole Clara thing is going it'll be something better but for me it's a missed opportunity with the reset button.