Not necessarily true. Core game design can vary, RE and FF being good examples. GoW can still be action game, Hell it blend action with a different to help add new mechanics. Metroid: Other M is good example of keeping the core but also delivering a fresh fresh oil change to how the game is played.
Well, since you listed examples of games that did change for the better (though it is arguable that RE changed for the worse). I'll list examples of games that didn't change and maintained or increase success & quality: Halo, Mario Kart, 2D Mario, 3D Mario, GTA, CoD, etc. I'll also liist game that did change and performed worse worse: Socom 4, Dragon Age 2, Resistance, etc.
As you can see, some games change for the good. And some change for the bad. Also, some stay the same for the good. And some stay the same for the bad. changing the core isn't that big of a factor for a game to mantain success. Changing the core isn't that big of a factor, in and of itself. The important thing is that the quality stays high and you allow enough time in between each installment. (Both of which the GoW has been achieving so far). If you're seeing bigger and bigger success critically and financially, that is not the time to change.
You don't just change for the sake of changing. Because changing does not necessarily cause or prevent success.. You change when your current methods begin to stagnate or fail. This is currently not the case for God of War. When God of War does start stagnating or failing, that is when you change. However, as of now, fans and critics love GoW's core, so it would be wise to keep the core the same.