Captain Jack and River Song need an adventure together. Period.
Of the "old" companions, Martha is really the only one that has any reason to show up again, assuming she still works for UNIT.
That said, Tennant's "final tour" in the The End of Time pretty much gave us closure for all of his companions. There's no necessary reason to re-open their stories.
Just going back to this post - it's interesting how companions now have 'closure', back in the day, many just disappeared in a couple of cases just blown out into space to die and be forgotten or left on a sofa!
Well, I think it probably has to do with the change in story structure. Where old Doctor Who would tell one long story broken up into multiple episodes, you could have one companion along for the ride and then dump him/her when the next big story begins. In that way, old seasons of Who are kind of like today's Christmas specials. The Doctor meets some new people, has an adventure, and then says goodbye at the end of the episode (like Donna in "The Runaway Bride" or Dumbledore Scrooge in "A Christmas Carol").
With the new seasons, we follow these companions on their journey with the Doctor for years at a time, and we [are supposed to] grow attached to them. For them to simply disappear would be very unsatisfying as a viewer.