Well that's why he killed himself at the end, but not before uttering "my vengeance ends now".
It was all about revenge, nothing more. Stories based of ancient Greek mythology always have a suicidal twist in them, and vengeance plays a big part in some of them.
Besides with the gods still alive after he went back in time to save his family he would still have to kill the gods anyway because they would continue to interfere with his life until they drive him to kill his family again.
The gods need to be dead so he can live or die in peace otherwise time travel or not he will never see peace. And if he went back and killed Zeus as a child then Kratos would not be born because Zeus is his father, so there is a barrier as to how far back he can go.
