Since both are natural, I doubt that overriding one with the other is always necessary. If I'm confronted with a female bear showing lots of teeth and a wee cub behind her, I'm pretty satisfied that System 1 thinking will be quite enough, thank you.You're missing the point, which is the fact that psychologists are seeking to override System 1 thinking in favor of System 2 thinking..
On the other hand, when I know that some blue berries can kill me, some are not only edible but quite nice, and I'm starving, I'm going to have to put aside System 1 for a bit and try to remember everything I know about which is which. This can get especially tricky if I find that I don't actually possess that information. Then I might have to invent some tests ("how about just a teensy taste, then see how I feel," and so on).
Or, how about when you're rolling dice hoping to win a little money (and are well behind at the moment). What do you really know about odds, and how will that help you decide what to do next -- double down and roll again or go home with the few dollars you have left and eat?