home experiment - Citric acid chelates calcium carbonate more than ethanoic acid, why does this result in a faster rate of reaction?

I performed an experiment using egg shells (calcium carbonate) to represent teeth and reacted the calcium carbonate with acids. When measuring the rate of reaction citric acid had a higher rate of reaction and from my research I saw that citric acid forms a more stable compound with calcium hence it chelates the calcium more than ethanoic acid.

In the mouth this would remove calcium ions from

$$\ce{Ca10(PO4)6(OH)2(s) + 2H+ (aq) <=> 3Ca3(PO4)2(s) + Ca^2+(aq) +2H2O(l)}$$ that equation hence the position of equilibrium shifts to the right so more tooth decay.

But with egg shells:

$$\ce{CaCO3(s) + 2H+ (aq) -> Ca^2+(aq) +CO2(g) +H2O(l)}$$

there is no equilibrium so if more calcium ions are chelated why does this increase the rate of reaction?