Loki's entire argument is pretty much going to be: The whole point is for the mission to be a success, right? Then why faff around with it when there's a quick, efficient way to get the job done. Particularly since it sounds like leaving Kidston alive isn't really going to do the "good" side any favors. Killing her achieves two purposes, in that it gets them into the room no muss, no fuss, and it also deprives the bad guys of a presumably valuable resource.

I want him to be in on this part of the mission since that's really the place he's going to be any fun to play in.

(And as I just realized, he can use an illusion to disguise himself as her as well...)