The input substrate to produce CaO is CaCO3. This requires a lot of energy, often obtained by burning coal and the reaction releases CO2. Absorbing CaO/Ca(OH)2 makes sense only in systems like submarines/bunkers with no external air supply. As a CO2 capture method on a large scale is makes no sense. Even if we think about using CaO as some "CO2 capture and release" material with who knows, storing pure CO2 underground, I think even theoretical no CO2 emitting energy needed for baking CaCO3 has a better use.