Since these ... ecosystems have persisted and evolved through enormous planet-wide changes ... I'm not worried
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.