The North Korea/South Korea demilitarized zone is a wildlife refuge. Native species have thrived in the area around the Chernobyl disaster after people peaced out. The Earth will soldier on.
We still have to deal with sea level rise, anthropogenic climate change, coral destruction, deforestation, because we have to deal with the effects. First-order effect of coral destruction is loss of habitat for fish, leading to collapse of marine species that use that habitat, leading to collapse of certain kinds of commercial fishing, leading to loss of livelihood and a food source for coastal communities.
Now is not a time for flippant comments about the robustness of life and nature "in general". Now is a time for very radical and drastic action to prevent even worse outcomes than the terrors which humans who are alive now are already guaranteed to face.
If the time scale of climate change matched the time scale of coral evolution, then your comforting thought might hold water. Unfortunately, our climate is changing faster than many evolutionary processes can keep up with.
Rates of change can matter. Just because you can safely walk down 30 flights of steps, doesn't mean you can safely jump off the roof of a 30-story building.
That's just the most recent and reliable example - we don't have the ability to measure such changes far into the past.