Personally, I find that the character in the new series is defined by his guilt and shame over the fact that he can always save the day and find solutions to all manner of problems through "creativity and ingenuity" yet when it came to the Time War the only thing that worked in the end was eradicating his own race.
I would agree that the show & the character had come to be defined by the Doctor's guilt & shame on the new series. Less so during the Matt Smith years but it was still there. And frankly, I'm sick of it. There have just been too many downers on the show in recent years. I mean, every time a companion leaves the show now, it's portrayed as a tragedy of earth-shattering proportions. (Except for Martha, but even that departure was pretty damn maudlin & melancholy.) It had become a show defined primarily by what the Doctor has lost over the years. Even when the writers gave something new to the Doctor, they only did it so that they can take it away later.
Well, to quote John Hurt, "NO MORE"! I like the idea that Gallifrey is out there somewhere. I'm not saying that the Doctor is going to find it anytime soon, nor should he. (It's possible that Moffat has more specific plans but I suspect that the Doctor won't find Gallifrey for at least another 5-8 seasons.) I just like the idea that the Doctor has something to hope for and something to move towards.
But then, I suppose I'm less bothered by this development then some people because I always figured that the Time Lords would come back in some capacity. (Heck, I was fairly surprised that it didn't happen at the end of "The End of Time.")