Its pretty obvious that you have missed the entire point of God of War, or you haven't played any of the previous games.
There is no higher purpose.
There is no desire to do good.
There is only revenge and hatred and guilt.
I agree it makes Kratos a slightly unpallatable character, but that is what makes God of War so different and special. Its good to play a character that just doesn't care and is so warped by his own guilt that he has become single visioned and doesn't give a shit about who or what gets in his way.
Its an incredible game. Its about as awesome as a game can be.