I don't believe there is much to explain. I watched a fantastic film and thought that the way Blunt brought Rita to life in it was flawless. Her act is great and she can sell both the "Full Metal Beach" and the human side without feeling she is playing on or the other, the stunts are amazing, she looks great but above all else she makes the character both brutal and elegant. She is threatening without being a jerk.
Anyway, I've seen people liking actresses for roles they haven't even played. Blunt's warm reception after Edge of Tomorrow seems quite reasonable in my eyes.