This article in The Guardian about the last episode of Dr. Who is a good example of why I don't write time travel stories. If you have not seen this episode and plan to watch it, stop reading now, because major spoilers are involved! Ditto for reading the article, by the way.
Okay, for those not worried about spoilers, companions Rory and Amy Pond end up in the recent past, in New York City where the Weeping Angels are causing havoc in the space time continuum to such as extent that the Doctor declares he can never go back there to that time again. When Rory and Amy get sucked back to NYC's past at the end, they become stranded. The Doctor flies off in the Tardis without them. What the Guardian article shows is an alternate ending where Brian, Rory's wonderful father, meets his grandson, who shows up on his doorstep (actually Rory and Amy's doorstep) as a grown man and hands Brian a letter explaining that Rory and Amy were trapped in the past and could never get back, but they wanted him to know they had a good life and by the way, shake hands with your grandson.
The article wonders why the ending wasn't filmed, as it would have provided some wonderful moments for the actor who plays Brian, and also some closure on the Ponds as companions. I think that's one reason why it wasn't filmed! Time travel stories don't have closure because the writers always want to leave a loophole to change things. Suppose Rory and Amy move to London and wait a few years. Could the Doctor come back for them then? What if more angels were to show up and suck them farther back in time? Could the Doctor rescue them then? Without closure, the dramatic present is still wide open, and I think the writers prefer it that way.
But not me. That kind of plot loophole just makes my brain hurt.