Ahh, the perennial question, "Why learn Latin (or calculus or whatever) in school if we aren't going to use it in everyday life?" My answer: "Why use exercise machines in the gym if you aren't going to use exercise machines in everyday life?" The answer is because the exercise gives you the strength and flexibility and skills you need to handle the physical challenges you do
encounter in everyday life. Studying Latin is the mental equivalent. It's strength training for your brain. It's good exercise for memory, pattern recognition, reasoning, and general mental discipline. It teaches you how to recognize the relationships between the forms and meanings of words, and that's good practice for understanding the vocabulary of any language or any pattern of interconnected forms or concepts.
Also, I don't think it's really possible to understand English spelling without having an understanding of the Latin and Greek roots of the language. English would be a tricky language for any non-native speaker to get a handle on, and the Federation has clearly never modernized or simplifed its spelling (which is hugely implausible, but never mind that). So some study in classical Earth languages might be helpful for aliens or other non-native speakers trying to get a handle on English. Or on human names for stars, constellations, etc., as well as the technical vocabulary mentioned above.