Most Western countries levy some form of CGT; to avoid it, you’d need to move to a low-tax jurisdiction like Switzerland or Singapore. It’s certainly possible for founders and investors to do that, but it’s a pretty big life change.
Moving from one US state to another, on the other hand, is pretty easy.
In the simplest case where the errors are Gaussian, this would probably be covered by standard regression lower bounds? You’d show that exponentials and sigmoids can be made close in L² over a restricted domain, then deduce it requires many samples / low noise to distinguish them.
Or as Aaro says above, maybe better to parametrise the sigmoid, and take the Fisher information of the turning point parameter.