I don't agree. The point is, anyone who makes the Carter argument will always come to the conclusion that the end is fairly near. Exponential growth is not a crucial logical component, it just means that you infer the end is very near. But the conclusion is totally unsupportable either way, because everyone will reach a different conclusion for the likely survival time, depending on when they are alive. For example, if Cain and Abel had used the argument, regardless of whether or not the growth is exponential at the time, they would have found it totally unbelievable that humanity would survive them by thousands of years. I say that an argument that is wrong when used by them is also wrong when used by us, as there is nothing to distinguish us. The other arguments against the Carter hypothesis are sound, but unnecessary-- this idea is logically DOA (even though it may be right, sadly, but for totally different reasons).

Put differently, if exponential growth is a crucial element, then the Carter hypothesis would argue that either humanity will die, or it will cease exponential growth forever. But if we populate the stars, of course we will see the return of exponential growth. We will have to have exponential growth again at some point, or we will die out (in millions of years, let's say).