I'm not sure exactly when almost the entire population was exposed to Mass but until Protestantism everyone heard Latin every Sunday and Good Friday and Holy Thursday and Christmas and Epiphany and Jan 1 and Cross-Quarter Day and..
Religion was, uh, crucial. Their whole lives were about the eternity after death. Why wasn't that enough to keep everyone speaking Latin?
Okay, the more they diverge the less pull towards Mass Latin the common speech will feel but how did it manage to get away from that pull in the first place? Anyway, the comedic end point is that from the Middle Ages to the 1960s Mass was looking at the priest looking away from you, using an alien language, singing Bible verses in alien, and everyone would have to sit through that to avoid Hell.