It's possible we don't have all the facts, but I'd think they wanted to have the operation underway as soon as possible because the random murderer himself wouldn't wait. It looks like Lenessia was only talking with the Kunie dude when the battle had already started. It could be they also wanted the murderous bastard to stick around and not try to flee when he was freed of his magic and thus the bothersome abilities. In the end the fact they did it this way also granted more experience to all the participants. Akatsuki even unlocked her first teaching.
Why? She hasn't been in any really serious, long fights before this, let alone a raid. The teachings would be worthless if one gained them by drinking tea with a princess. The others probably had more stressful incidents under their belts. Although I suppose there could be teachings related to non-combat classes/skills that one could unlock by whatever methods. For all we know Nyanta already has an Iron Chef teaching unlocked...
Akatsuki's development pleases me even though I can't with any honesty call this arc good. The teaching aside, I like what this did to her personality. The socially inept Akatsuki was cute her own way, but from what I can see, this new, more forward Akatsuki also has considerable charm when she's awkwardly trying to express herself and socialise.