If you're willing to accept inputs that are only almost exactly the same, there's already a class of deterministic systems that can provide you with wildly diff

If you're willing to accept inputs that are only almost exactly the same, there's already a class of deterministic systems that can provide you with wildly different outputs. Moreover, in such systems, the output might be impossible to predict based on the input (other than by running the system). Deterministic doesn't necessarily imply predictable. I'm just saying, you don't need to reach for quantum mechanics here, living organisms (and computers) are quite capable of being unpredictable even without it. For the rest I agree with you.