Like BillJ said, it adds nothing and in my opinion would have caused some sort of tone mismatch. It had been tragic up until now and slowly descending into wrath on part of Spock. To suddenly make it a rescue mission would shift the tone to a more hopeful one and I think this sudden shift would damage the movie. Besides...
What if we get the Enterprise positioned over the Vengeance, lock onto an area of the saucer section with the tractor beam and use every working engine left to push the Vengeance down into the Ocean?
The Enterprise was barely holding itself together, and it's expected to match the Vengeance in velocity by flying over it? I don't think it can even reach the Vengeance at that stage.