If Clara hadn't intervened this would have been the Fall of the 11th Doctor. The Silence didn't want the Doctor to live to open the door and let the GH undo all of the Doctor's victories and leave the Universe in ruin. It was better to kill him early than to have his previous battles undone.
I get that. I guess I just figured that the Silence would actually be there. If all else fails, Trenzalore would be their one last chance to stop him.