Personally, I'm not sure it makes a whole lot of sense it's Kira, but that's what Cryptic decided and it's their game.
I agree. It makes sense on some levels but it is also rather contradictory. On one hand, she has had extensive contact with the emissary and knew him for several years. She was also very dedicated to her beliefs and her religion. What I don't understand is how a member of the Bajoran militia, a soldier, becomes a politician/religious leader.
It's pretty much certain that by the Foundry EULA Kai Kira can't be used in missions. A pity that we can't use the Kai in our missions. The only possible solution I see is that Cryptic elects a new Kai