But if I take a population that dies out, any population that dies out, in my sample, then the geometric average becomes 100% loss. There are definitely cases where the geometric average also gives a weird answer.

(I'll also note that their headline number changes quite a bit year-to-year, as they expand the dataset and fiddle with how important they treat each part.)

I strongly agree with the base dataset - I just don't understand why this is the best indicator. If we care about total population, we could just compute with the sum. If we care about how many populations are stable/growing, those numbers are also easy to get from the same data.