Latin is taught in some schools, but required in very few. There is an elite college preparatory high school in Cincinnati which requires 3 years of Latin, but they cant give you a good reason for it. It's really a rite of passage, a "binding" hurdle that the students jump over together. And when they get into my classes, and I adduce a Latin example, it is the students from this high school who groan the loudest. So I have to try to convince em that Latin actually is interesting.
Actually, the words in the quote from Leibniz are NOT cognate with the English words you may think they are. All but one of them are LOANWORDS, borrowed directly into English from Latin or else via French. The only word in your quote that has a direct cognate in English is est -- 'is. It is cognate with English 'is' and German 'est' (and Russian 'est, &c). Now, I dont know what you mean when you ask "How prevalent would this be?" Would what be where?
Many cognates that Latin shares with English are not easily recognized. pater ~ father, pro ~ for, piscis ~ fish, cors/cortis is cognate with English 'heart'. Latin tres is cognate with English 'three" and German 'drei". The English words 'paternal and triplet are BORROWED from Latin. But 'father' and 'pater' and 'three' and 'tres' are descended in their respective languages from the original prehistoric *ProtoIndoeuropean Language's word for these things.
Sooo. if your purpose in compelling childredn to study Latin is so that they recognize Latin and French loanwords in English, why not just give em a course in Latin --and dont forget Greek--roots in English? There is no need for them to learn four verb conjugations, 5 and two halves cases, &c to just learn to recognize Latin and Greek roots in English. The study of the grammar of Latin is all but useless for that.
Some literarily "educated" people once argued that students should study Latin because it has a case system and "teaches people to think". Well Hungarian has a lot more cases than Latin does; if that's the purpose, then we should make Magyar mandatory -- nice alliterative slogan too! And there is no particular evidence that learning a case system per se somehow teaches one to "think".
Latin of course opens many literary works to a student of classical mediterranean civilization -- but that's a utilitarian venue of the language, and most of those works have been translated by far better scholars than a student with two or three years of high school Latin is apt to be. So that's a pretty lame reason. Study of Latin and Greek might help a Christian who's interested check modern translations of the church documents such as the Nicene Creed and see how many contemporary denominations use a mistranslated version of it.
But there are and have been other civilizations besides classical Roman. Japanese, Chinese, Sanskrit, Persian, Maya, Javanese, Aztec...... Latin wont help you a bit with those.
Study of any foreign language is a mind opener -- especially if that language works rather differently from one's own native language. In this respect, Lamut, Lettish, Lithuanian, Lakota, and Lenni Lenape are just as useful and mind opening as Latin. Indeed Lamut, Lakota, and Lenni Lenape probably even more so. And Lithuanian has more cases than Latin. Lamut still more though.
There are some good linguistic reasons for studying Latin. It was typologically unstable at its Classical period so we can study a language in the process of major change. Anybody interested in the Romance languages certainly will find Latin helpful and it's virtually indespensible if one wants to be a good Romance historical linguist.
But much of European and all of North American societies have found it no longer useful to require Latin of all educated people and people now who seriously claim that a person isn't educated unless they know Latin are generally regarded as silly snobs.
U of Cincinnati
Dept of Anthropology