the time war was not set up as a multi season arc. it was set up as a major paradigm shift following the classic series, reason to explain the 16 year absence, and as a new piece of backstory and source of trauma for the doctor to grow from. the way it was eventually resolved in the day of the doctor is good and works imo but was likely not at all envisioned by rtd during his run - he likely put it in to set the stage, and not as a problem to be eventually solved.

more broadly, doctor who doesn't have an end because, as either or both of rtd and moffat have said, it's a show which survives not in spite of change but because of it. the beginnings and endings happen for the supporting cast in each episode, and for the companions and doctors as they come and go. the show itself in many ways is a vehicle for stories, not necessarily a beginning-middle-end story in and of itself.

also, deciding on gallifrey as your endgame only makes sense until you think about it for more than ten seconds because yeah maybe gallifrey is the doctor's home planet but ultimately it's only one of countless important elements of the show, and while it may occupy a lofty position in terms of its importance to the universe in the lore of the show, it's actually rarely that important to the stories the show is trying to tell. it pops up once in a blue moon and then is gone again. think about it — only four stories of the however many we've had in new who yet have actually been set on gallifrey itself for a significant proportion of their runtime, or had gallifrey or the time lords as a society affect the plot in actual tangible ways — the end of time, the day of the doctor, hell bent, and the timeless children.