I'm not sure I understand where the carbon savings comes from. The cement industry specifically needs lime, CaO. Lime is most easily obtained by burning CO2 off of limestone, CaCO3. As you point out, this is effectively "burning off" captured carbon dioxide and is bad. Where does the carbon savings come from when the ultimate destination is to just burn CO2 off and make the actual desired product, CaO? Is this proces…
Yep, exactly! The world needs CaO for cement. We have a carbon neutral process for making it. It's actually overall negative as not all carbonates we extract are usable in cement production. But as far as cement producers are concerned it's carbon neutral.
You do the same with limestone, rapidly creating it by capturing atmospheric CO2 (indirectly, via the ocean) so it can then be burned in cement production instead of the naturally occurring kind. In both cases, CO2 is released into the air at the end when the product is burned, but because the released CO2 had just now been sucked out of the air anyway (instead of having previously been sequestered in natural limestone) you're not adding to the total amount of CO2 in circulation in the system, making the process neutral.