But this is just a criticism of extrapolation beyond support, not of any particular class of model. The extrapolation would be equally nonsensical with a linear

But this is just a criticism of extrapolation beyond support, not of any particular class of model. The extrapolation would be equally nonsensical with a linear probability model or any sigmoid transformation, because in reality the problem is only defined within a support (or else is a hinge problem, where everything outside the support has a fixed value). This doesn't make the model useless, it makes it useless for particular out of support extrapolations. This is why inference is both a quantitative and qualitative problem.