We don't even get a "There's not much power!" or anything as to why the Enterprise didn't try and prevent the Vengeance from crashing. They just sit there.
That was a big problem. They stop the Enterprise from falling and then they waste 5 minutes to watch Kirk die. In the meantime, the Vengeance falls to Earth as well (and why exactly did it take 10 minutes longer than the Enterprise?), and they do nothing to stop it.
Are we really nitpicking for the sake of it?
Sulu and the bridge crew simply didn't have the Vengeance on their mind. After all, their (and the audience's) focus had been on the Enterprise desperately trying to survive. And immediately after that, their captain dying.
The fact that you mentioned the Vengeance barely missing the Enterprise showed that nobody remembered it was there. They are only human, even robots like Data wouldn't be able to recover from such a serious incident so quickly, in 5 minutes. Do you know how short 5 minutes is?