I'm jumping in late here, and haven't read all the posts, but heres my two cents.
First of all, this choice is foreshadowed in haven. When talkling to The Iron Bull, he talks about how the Qunari pick their leaders by choosing those who are willing to make the tough decissions and live with them.
Second, the Qunari have never had an alliance with anyone. Ever. The Inquisition (if you choose to save the dreadnaught) is the first. This shows that the Qunari are not set in their ways entirely, perhaps this alliance can help change their minds about those outside the Qun. After all, the Qun is a religious text that is interpreted by the Ariqun, maybe the Ariqun decides "oh these guys aren't so bad after all, lets stop being giant horned jerks". In fact, I wonder if its only the military that demands such focus that they all seem stoic and whatnot. The Iron Bull says that they ALL give eachother nicknames under the Qun, which shows a feedom of thought and expression. No, they don't get to choose their own jobs, but the ones that choose the jobs seem to be good at their jobs. And I have a feeling that if a qunari thinks he can serve the Qun more effectively in another role, he can request a job change.
Thirdly, this all takes place after you gain the ability to open rifts that suck up bad guys. WHY NOT JUST DO THAT!?!
Gatt: "You need to do whats right Hissrad, for this alliance and for the Qun"
The Iron Bull looks at the inquisitor
Inquisitor: "This is why people don't like the qunari, you don't think outside the box." *opens fade rift on beach
BAM! Chargers saved, alliance intact, and you taught The Iron Bull a little something.