But having an s-shaped curve is not the same thing as being a sigmoid function, in the same way that having a bell-shaped density is not the same thing as havin

But having an s-shaped curve is not the same thing as being a sigmoid function, in the same way that having a bell-shaped density is not the same thing as having a gaussian distribution. There a tons of processes out there that can approximate well with either of those two, while being extremely different in extrapolation. One thing that can immediately disprove mathematical sigmoid modeling: curve symmetry. If the early adoption exponential growth is not exactly the same shape as the late adoption slowdown, then you don't have a sigmoid function. And that's the problem: if you're using a single function to model the result of two (or more) separate processes with distinct mechanics and parameters, you're going to have the same exact pitfalls as you would trying to model a bimodal process with a single probability distribution. Namely that they might fit well with interpolative methods, but completely fail with extrapolative methods (like forecasting!).