Your argument doesn’t make sense to me. You’re saying the exponential models things “locally”, but then so can a sigmoid. You say an S-curve won’t actually be an S-curve, but neither will an exponential. An exponential function that fits data is not that much simpler than a sigmoid function, and importantly the exponential will be wrong in a non-specific way (we just know that after some unspecified point exponential growth will break down). The sigmoid is at least wrong in a specific way that allows us to say something about where we made a mistake in modeling how growth will end (and because growth always eventually ends, failing to model it is making an incomplete model that clearly confuses a lot of people, because there’s no end to people who act as if the growth of something will never end).
Your argument doesn’t make sense to me. You’re saying the exponential models things “locally”, but then so can a sigmoid. You say an S-curve won’t actually be an S-curve, but neither will an exponential. An exponential function that fits data is not that much simpler than a sigmoid function, and importantly the exponential will be wrong in a non-specific way (we just know that after some unspecified point exponential growth will break down). The sigmoid is at least wrong in a specific way that allows us to say something about where we made a mistake in modeling how growth will end (and because growth always eventually ends, failing to model it is making an incomplete model that clearly confuses a lot of people, because there’s no end to people who act as if the growth of something will never end).