3. They Can Expand The Mythology
As the series keeps going on and on we keep seeing new changes and new elements being introduced to the current mythology. For example, the introduction of The Moment a sentient weapon capable of altering reality and crossing timelines or the recent theory that at the end of a Time Lord's lifetime they can come back to a previous form proves that the Time Lords represent all sorts of opportunities for narrative jiggery-pokery and potential mythos expansion. I'm pretty sure that with a race which has existed since the beginning of time, we haven't seen even one-tenth of their story or mythology. Imagine what kind of stories or events or characters have left their mark in Gallifrey's story, let alone the universe, if we're allowed. But not only that. So far the Doctor has been considered an outcast for he people of Gallifrey, now he's their savior I'm sure they'll probably tell him more knowledge and information that were previously unknown to him. Whatever the case might be, it would be quite interesting to see the Doctor or any other character for that matter interacting or encountering new objects or elements in the species' history that changed the universe forever.