The cartoon that you made me look at makes no mention of equilibria.
But Wikipedia present a reasonably simple demonstration of the effect of buffering (http://en.wikipedia.org/wiki/Carbonic_acid)
For example, an atmosphere with 350 ppm CO2 over water will produce a pH of 5.65. If that is tripled to 1000 ppm CO2, the water will indeed increase in acidity...to a pH of 5.42 (negligable change). Likewise if we engage in Algore’s wet dream and decrease atmospheric CO2 to 100 ppm, the pH rises to 5.92.
But over this whole range (100 ppm to 1000 ppm CO2) the carbonate ion concentration changes by 0.7%. Your cartoon is incorrect in that it suggests that more CO2 will result in less carbonate ion...the opposite is true, but the reality is that more CO2 will have only a negligable effect.
The biological effects of algae or pollution would be far more significant. Local temperature variations (El Nino, etc) would also play a larger role. But blaming coral death on a carbonate ion shortage, from MORE CO2, is laughable.
The seawater alkalinity system, largely (but not completely) due to the carbonate equilibria, is why this happens.