If you tell me that there is no reason whatsover that the Doctor would ever want to get Gallifrey or the Time Lords back, I will rip a whole through time and space and punch you in the face
Now I’m not saying that the Time Lords were all perfect, they really did some horrible stuff (The End of Time et al.) and if they’re actually saved by the Doctor, they’ll have to change a lot if they want to avoid being anihilated again.
However, during all the RDT era, the Doctor clearly expressed guilt over what he’d done, nostalgia, deep sadness over the fact that he was the last of the Time Lords (- so please don’t tell me that Moffat invented it all.). He clearly missed his planet (just look at him in Gridlock when he’s talking about it to Martha) and his kin. I acknowledge that in all Classic Who, the Doctor was shunning the Time Lords because they’d done pretty nasty things to him.
But home is not about the douchebags that made your life hell. Home is about your family, your friends, the place you grew up and played and learnt, the moments of joy shared with the people you love, all those memories that are seared into your heart(s) forever and that make you smile when you remember them.
What I believe is that the Doctor isn’t looking for Gallifrey to revive the specific Time Lords who ruined his life. He’s looking for Gallifrey because to him, it’s home.