Joss Whedon and Marvel made the right choice in cutting this out.
I have problems with the opening of The Avengers. So did Marvel and Joss Whedon, it seems. They apparently wrestled with how to open the movie, and at one point they had the above sequence at the start - a very grim, very dark way to open a movie that is anything but grim and dark.
Watching that I have to wonder what the other half of the wrap-around is. If the entire film takes the form of Maria Hill recounting the story to the shadowy SHIELD leaders, there has to be an ending. She seems like a real horrible bitch here, so I would guess that the ending is a switcheroo, with her actually being chummy with Nick Fury after supposedly reporting him.
The opening itself is gripping, and it does cast the ending action in a whole new light - but the wrong light, I think. Avengers 2 can open with someone complaining about the destruction and death toll of the invasion, but the movie itself needed to end in triumph. Having this scene at the beginning of the movie would have shaded everything that came after as a pyrrhic victory. I believe that the film's positivity is what allowed it to beat the hell out of The Dark Knight Rises at the box office, and this opening would have undermined that.