Think about it, if Kratos went back in time to stop himself killing his family then he would have to kill himself to save them since talking himself out of it is not possible since Ares used his powers to enrage Kratos and make him loose clarity and control. If he killed himself in the past he wouldn't exist in the future and so then who else would be there to put an end to the tyrannical, corrupt and manipulative rule of the Gods?

Also even if killing himself in the past doesn't kill his future self, Ares would still have been pissed at him for rebelling and would probably have just killed Kratos' family himself because he's an arsehole.

Plot hole mystery solved, I'd say. I love the story in the God of War games, right up there with the best games (I love Greek Mythology and SSM's take on it) and there's so much to analayse. 

That time travel thing created a million plot holes. He could've killed Zeus as a baby or done as you said or saved his mom or stopped himself from pledging loyalty to Ares or gone and partied with Homer who knows

i would have to play it again to be sure, but does he really have access to every past?

or is it rather that he has access only to certain events in the past?

...on some alternate powerful hardware ...

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.

Would have been better if his character and VO are not so annoying, the gameplay hasn't really changed since 1, the plot is just "I'll kill you all!" like any beat them up game and he screams it out loud too like a little kid in a man's body proudly I guess. The games look nice for their times though, that's really the highlight to God of War. There is no real plot even if you like greek mythology, I can throw anything in there from other cultures and the plot of "I'll kill you all unless you let me bang you!" still wouldn't change. That's the veritaz brah!

PS: I also have no idea where Mario came from, how do you compare a platformer to a beatem' up? At least I can take a baseball bat to people in GTA4 and a giant dildo in Saint's Row the Third even though they are open world shooters.

My thoughts are...it's just God of fucking War man, who cares?

In case you didn't know yet, I was playing the demo for Ascension. :P You should go try it out right now! And the spoilers are from GoW 1-3, but really mostly 2.

ohhh the demo! and hell no! i wont play it!! why should i play it then have to wait 2 weeks to continue it? ill just wait until i play the full game

Simple answer really if he goes back in time and stops himself from killing his wife daughter then  he will never seek revenge against the gods and will never gain time control in the first place.