While if instruction in Latin was "universal", certainly by age 10 kids would have a good grasp of it. Having said that, Latin fell out of favor once literacy became widespread. Nobody spoke Latin, and it's only use outside of academia was the Catholic Church - which as literacy spread had already lost its exclusivity to other branches of Christianity that prayed and preached in the vulgate.
Given that nobody used Latin other than these academic or religious reasons, and the reality is that while there will be many folks literate in the local language, there will always be fewer literate in Latin. When the overwhelming majority of the relatively small literate population read Latin, it was surviving for that use. Once those that are Latin readers (at least) are a ever diminishing minority of the literate, local languages take over.
English has to a large extent the role of Latin, though not as completely, in part because English is not just a language of scholarship but also of business (and aviation, and other uses).