I completely see (and share) your reasoning. But I think it’s very anthropocentric.
There is nothing human-centric about life wanting to continue.
Horseshoe crabs haven't changed in 250 million years. What's your opinion on them "stopping the cycle"?
We people value our continuing existence, and I share that sentiment! But it's by definition an anthropocentric perspective.
But I think the point here is that we wouldn't be "doing good" necessarily by preventing a mass extinction; we would be definitely doing good to ourselves (no small thing) but for Earth's ecosystem? Debatable. Especially since we would possibly be preventing the spread of new species, since mass extinction events seem to have been so far useful tools in evolution's toolset.