You are making a lot of assumptions there. We've already seen via the twitch stream videos that certain operations are exclusive to certain advisers.
Obviously Josie isn't an option since this isn't a diplomatic mission.
Hell, considering both Cullen and Josie are love interest, they are probably both safe from this fate.
I mean going by what we know, Leliana was captured because she was infiltrating them, because she's our spy. If this is an infiltration mission, then obviously we can't pick Cullen or Josie.
Especially not Josie, who deals in diplomacy.
In the E3 redcliffe demo they say you ''chose'' to send Leliana there, which implies that there are other choices. Such as not making this an infiltration mission perhaps.
Also, after everyone went batshit crazy thinking Sera and Bull died, they said not to look into it too much and that this outcome was one outcome out of a whole lot of possibilities, some from past choices.
Who knows, Connor being possessed might have an impact on that quest. You could have killed Alexius during a previous mission! Or maybe, as I'm inclined to believe, you can send other advisers. I wouldn't write of Josie as a possibility for this mission. What if the Venathori pretended to be willing to reconsider their stance, or at least to agree to a truce?
Of course i'd never ever risk sending her she's too pretty (even though Dorian is my romance), and Leli was my DAO romance. Cuuuuuuuulleeeeennnnn? I need you for something!