What controls the acidity of the ocean?
You have focused on corals (that have a much more lower biomass than for example foraminifera), and you have forgotten what controls carbonate levels at oceans at bigger scale is Henry's Law:

&quot;In chemistry, Henry's law is a gas law that states that the amount of dissolved gas in liquid is proportional to its partial pressure above the liquid . The proportionality factor is called the Henry's law constant&quot;
Source: Wikipedia

So answering your question what controls acidity on oceans is indeed carbonates, but it is atmospheric $\small\sf{CO_2}$ levels (and temperature, as Henry's constant is temperature dependent) what determine the concentration of carbonates.
The quaternary increase of $\small\sf{CO_2}$ leads to the generation of new $H^+$ and thus acidify the ocean, acording to the reaction:
$CO2 (aq) + H2O ⇌ H2CO3 ⇌ HCO3− + H+ ⇌ CO32− + 2 H+.$