We still aren't exactly sure what it was about The Doctor opening up his own tomb that triggered the events of their prophecy; we're not even sure that those events have actually been averted or are yet to happen. Key elements of the prophecy do not seem to match up with the events of "The Name of The Doctor".
So it's premature to think that it was only the Great Intelligence's actions that The Silence wanted to prevent. It may be that, if the GI were removed from the picture, that someone else would come along and try to do the same thing. It could be that there's something else in The Doctor's tomb, or some other event that could occur by accessing his historical time stream, that causes problems.
Remember that, in the episode, The Doctor points out that he has time traveled more than any other person in history (and when The Doctor says "in history" he's probably including all of future history, too.) This means that, while in theory all Time Lords or other time travelers probably have similar phenomenon in their tombs, his is by far the most powerful and most dangerous.
So, the most likely answer is that The Silence need to be absolutely sure that no one can get into the tomb; the easiest way to prevent that is to remove the only person with the knowledge to enter it. Yes, River also knows how to get in there, but we also don't know when she actually learns his name, as she did not actually learn it when they got married. Likely The Silence are trying to eliminate The Doctor before he can tell anyone else that secret.