Well, it does look that killing a big species is like freezing a body to absolute zero.
I am ready to buy that 0%-10% killers are distributed according to the promised power law, if you buy that reducing human population from X to kX costs -log k. Note that this doesn't alter your observed power law at all.
Why this? Because you have to be stronger than random resistances (due to genetics, lifestyle, health conditions etc.) present in different slices in populations.
Also, any virus will evolve while it infects a billion humans; there is a pressure to spread better and leave host alive.
And long incubation period cuts both ways — either you are stealth for years, or you are spread by air next week.
The FHI's mini advent calendar: counting down through the big five existential risks. The fourth one is an ancient risk, still with us today: pandemics and plagues.
Pandemics
Current understanding: high
Most worrying aspect: the past evidence points to a risky future
The deathrates from infectious diseases follow a power law with a very low exponent. In layman’s terms: there is a reasonable possibility for a plague with an absolutely huge casualty rate. We’ve had close calls in the past: the black death killed around half the population of Europe, while Spanish Influenza infected 27% of all humans and killed one in ten of those, mostly healthy young adults. All the characteristics of an ultimately deadly infection already exist in the wild: anything that combined the deadliness and incubation period of AIDS with the transmissibility of the common cold.
Moreover, we know that we are going to be seeing new diseases and new infections in the future: the only question is how deadly they will be. With modern global travel and transport, these diseases will spread far and wide. Against this, we have better communication and better trans-national institutions and cooperation – but these institutions could easily be overwhelmed, and countries aren’t nearly as well prepared as they need to be.