Cockroaches are small. Note that most of the animal species that survive mass extinction are small.

Also, ocean warming can trigger anoxic events which release hydrogen sulfide which can suffocate entire coastlines and also attack the ozone layer affecting life everywhere. The worst case feedback loops are nightmarish.

And it would also be nice to avoid the not-even-worst case where civilization is reduced to some isolated enclaves clinging on with their bare lives.