Having Murph run after Cooper when he's driving away, serves as an extra little push, an extra little reminder that their conflict is left very unresolved. (And also kept my tears coming.) And because of Cooper's situation, we have to carry all this tension and heartache with us through the rest of the movie.
The conflict gets touched on again and again. It changes, it stretches, it deepens through the show. (It can't just stay the same, because it would go stale and dull our sensitivity to it). It hits a climax with Murph when she yells that Dad didn't even try to save them, that he left them here to die, and hits a climax with Cooper when we see he would give anything, anything to go back and change his decision to leave Murph in the first place.
Imagine instead, that Murph had ran out and caught up to them, and they'd had a sweet loving goodbye, and later, Murph begins to think Cooper abandoned her. It would not have been near as effective. The emotion would not have felt near as powerful, near as raw through the movie.
So, if you're a writer, look for powerful conflicts to leave very unresolved.