Millenia like in with trees, that a forest fire can return it to the atmosphere in a whim? How stable are those calcium carbonates regarding how the oceans can change on temperature, acidity or even life, to name just a few factors?

And it should be able to address more than this (https://elements.visualcapitalist.com/the-scale-of-fossil-fu...) amount of carbon yearly (and that is not the volume of the calcium carbonate, but the source carbon, it could be far bigger).

Keeping the fuel underground is the best capture technology. It will keep being safely there unless a suicidal species dig around for retrieving and burning it.