You are certainly correct that there is limestone rock and that it derives from skeletons of diatoms etc..
Consider this (caricaturized) argument: suppose most artificial mummies are mummified humans, that does not mean most humans end up mummified!
please check out the sibling comment by philipkglass, the referenced text has a section on calcite compensation, and the previous section detailing the saturation horizon. At high enough pressure calcite prefers being dissolved again.
Consider a calcite diatom cap, close to the beach, since it is above the saturation horizon, it won't dissolve soon, now consider a diatom dropping dead over the mariana trench, so the calcite starts sinking, until it passes the saturation horizon, now the pressure is clearly high enough to prefer being dissolved...