I think I see what you're saying, you're saying that if you wanted to try and apply Carter to other species, perhaps go out and take a census of all the living species on Earth for example, right now, then you would not be able to conclude that only 5% of the species were in their first 5% in birth order. In your example, you say what if all the populations have exponential growth prior to total extinction, then the vast majority of the species you would encounter would be early in their growth because we are sampling at a random time. The only time you can know the population growth behavior but still apply the Carter conjecture is if you are applying it to your own species, such that you are a randomly chosen life no matter what information you have about what the distribution is doing. I think you are right about that.

Here is another wrinkle though, if we want to restrict ourselves to the thread that we have no useful information about our survival so we may as well apply Carter, probabilistically. To what extent can we count ourselves as a random sampling from all of humanity? Could our genes come at any point along the way? Indeed, what if humans start doing genetic engineering on the genome, such that you or I would be impossible 10 billion humans from now? So the Carter conjecture might not hold simply for extinction, in the case of intelligent life it may only hold for the time it will take to alter the genome such that you are I are no longer a randomly chosen life over all humanity. Put differently, there has to be some criterion for constraining what the selection is occuring over. If we can count future human progeny that is even minutely different from you and I, then where do we draw the line? How much similarity to us is required for it to count in the Carter selection process?

And here's yet another wrinkle. If the elegance of the Carter conjecture involves the sentience of the being doing the reasoning, which seems to be a necessary part of "selecting a life", then did you have to be a man to count? In other words, was your life selected from the lives of all humans, or just human men? This speaks to the question, could you really have been any human, one life selected at random, or did you have to be exactly you, a single individual who won an unbelievably unlikely lottery to even be here at all?