Although people toss around ideas of why Latin is beneficial, such as it helps with medical or legal terminology, or helps you understand etymology, those things can be learned without becoming a fluent reader in Latin. The benefit of learning to read Latin is that you know how to read Latin; in other words, you have access to the texts in the original language.
Similarly to French, I think Latin enjoys a kind of vestigial prestige from earlier times when knowledge of it was the mark of an upper-class education. Universities are no longer primarily for training clergy and/or providing polish to the elite.
By the way, I went to a Catholic university which used to have entrance requirements in both Latin and Greek. This was at least a couple decades before my time, though.
I strongly suspect that in previous centuries the main benefit of learning Latin was that it meant you were a gentleman and could enter certain professions only open to gentlemen. From my understanding of Victorian literature, about the only high prestige profession you could attain without much education was engineering. That profession was open to anyone with ability and drive. Stereotypically, the professions were the law, the church, medicine, the military and the navy. I do not suppose you needed much Latin to be an army or naval officer. To be a naval officer you needed to start young and have a head for mathematics. For at least the first half of the century army officers bought their commissions. I think they just needed to be posh and to be brave. You needed Latin, and preferably to have gone to university to enter the law or the clergy. I am not sure what the situation was for medicine. There were different types of lawyers and doctors, some more prestigious than others. There were other professions that were close to acceptable for upper middle class folk: school masters, forerunners of the civil service, gentleman farmers, banking and finance, merchants. To get into most of these professions, I expect you needed to be middle class, although maybe not very middle class. That meant you needed a reasonable education, which meant studying Latin, whether you retained much of your Latin after you left school or not.
Speaking of Victorian literature, many of the most prominent Victorian authors were not very middle class. William Makepeace Thackery and Anthony Trollope were. Charles Dickens and George Eliot were lower middle class. Charles Dickens would have had some Latin. I do not know about George Eliot, as I do not know if girls were taught Latin in school. The Brontë sisters were daughters of a clergyman, but not very rich. Patrick Brontë would have known Latin, but I do not know if his daughters did. Thomas Hardy's background was working class. His father was a stone mason and his mother was a servant. He wrote a book called Jude the Obscure in which a farm boy studied Latin in order to go to Oxford university, but he was still a rustic so he was not accepted. Elizabeth Gaskill wrote a book called North and South in which a mill owner paid for lessons from the heroine's father, who had been a clergyman but had lost his faith. The mill owner had had to leave school early, and wanted some tutoring in the classics to take the rough edges off.