I don't buy it. The current mass extinction event predated industrialization and the intense population that it sustains.
Somewhere around 500 million - while still capable of massive environmental damage (we're looking at {probably way}
less than 200 million during the destruction to the med region) - anywhere above this is when the damage really
started to accelerate. That gets us to pre-industrial numbers. If we can maintain a technological society with that
footprint, I would have high hopes for humanity.
And, it's not like we'd need to do a mass kill off. There's a tipping point (and we may be over it) where Methane stores will render
global warming likely to finish off this iteration of society, but if we could do the politically untenable things like cutting emissions,
reducing industrial meat production, ect, in conjunction with mass sterilization, the overall cost would be lower. But, humanity's
responses aren't designed for such foresight. The species would need to undergo a massive transformation - which is probably
impossible without calamitous (for us) natural goads. Evolutionary 'advancement' is a craps game.