time travel - What was the point in the Silence trying to kill the Doctor when Clara saves him anyway?

It has not been said how aware the Silence were of the events that transpired on Trenzalore in "The Name of the Doctor". They may not even know of the Great Intelligence's and Clara's involvement in the matter, and could just be afraid of what the prophecy implies. In "The Wedding of River Song", the Doctor modeled the situation that he was in to Winston Churchill:

Doctor: "Suppose there was a man who knew a secret. A terrible,
dangerous secret that must never be told. How would you erase that
secret from the world? Destroy it forever, before it can be spoken."

Churchill: "If I had to, I'd destroy the man."

Doctor: "And silence would fall. All the times I've heard those words,
I never realised it was my silence, my death. The Doctor will fall."

Considering this, it seems that the Silence's goal is not specifically to prevent the damage caused by the Great Intelligence corrupting the Doctor's timeline, but rather, to prevent his "terrible, dangerous secret" (which is now known to be the forgotten version of the Doctor portrayed by John Hurt) from being revealed.