This is not the case. You only need a Ca-bearing system susceptible to leaching by supergene/meteoric or hypogene/hydrothermal fluids. It could be also a metabasic magmatic rock or on older geyserite or something else. The prerequisite is the adequate PT conditions, e.g.pressure release and/or temperature drop. Carbon limitation is not the case in near-ambient aquatic systems and the atmosphere under mid-latitude climatic conditions . Under near equatorial regimes sulcretes (S), halcretes (Cl) ..may form instead of carbocretes under supergene conditions. Under polar ones the system is blocked by the solid state of H2O and rarely ikaite/glendonites may form < 8°C (metastable). Convert to calcite later.