And in the same story, the man actually sits in and operates a time machine, which supposedly he himself has built in the future. And at no point does he consider, "Hmm, fascinating, suppose I ask my own ship how to engineer a time warp, either back to warn my home planet, or forward to stop the future guy from warping back." Instead, it's decided he'll bottle up his emotions and bury his feelings.
Old Spock's ship is not a time machine, it just carries the Red Matter weapon. The time travel in the movie was completely unexpected and uncontrolled. Nero and Spock fell into the same black hole seconds apart in the future, yet emerged 25 years apart and in different locations in the past.
Remember that in prior Star Treks, they've been able to time travel by warping around a star (STIV), modifying a deflector dish (ST: FC) or even in one DS9 episode by using the transporter - yet these things are never brought up as a means to fix anything that goes disasterously wrong. When the Federation was about to lose the Dominion war, no one mentioned going back to undo "Emissary" and warning everyone.
So yeah, there's an Imponderables clip in it, but it'd be one covering the entire Trek franchise.