What an interesting thread in terms of the spectrum of opinions!
To a previous poster who's a Latin teacher and was curious about if people who'd studied the subject thought it was useful, here's my two-pence.
I grew up bilingual as my mum is Italian, so when I started Latin causally at school I found it extraordinarily easy. I was one of those weirdos who did it to a full A level; when I was studying it I found translation easy, and always lost marks in the analysis sections which was more like writing an English essay on the theme etc. Basically, not to blow my own horn but I can get by pretty well in Romance speaking countries due to either the Italian/Latin/French I grew up speaking/studying respectively. Although there is the question of chicken or egg in the sense that, growing up bilingually, I probably have a better sense or shared words/etymology regardless of the fact I studied languages formally, but the formal education helped.
Flash forward to now...so I'm a junior doctor, and it's often said to me 'oh studying Latin must have helped you'. Well, in my experience, not really. Yes lots of medical terms are in Latin, but I don't speak or interpret Latin, I merely pepper medical conversations with Latin words to sound clever, and often avoid using them completely when talking to laypeople (i.e. patients) because that's part of good communication. My OH is also a doctor, is not particularly confident with MFL, definitely didn't do Latin and yet they do not struggle when we talk about our work including the Latin/Greek terms that are involved. At the end of the day, me saying Sella Turcica when I talk about anatomy is a bit pointless unless you know the context about which it's placed, and also at med school we were taught that it translates as Turkish saddle because that's what it looks like, which reduced my 7 years of Latin study to about 10seconds of focussed teaching.
So to people who says it helps with certain jobs that still uses Latin phrases, I would possibly disagree based on my experience. However, I think the benefits do include a certain grounding in linguistics, as people have discussed the ability to think logically which has applications from programming to code breaking, and interestingly, what no one else has talked about, is the civilisation aspect. Outside of finding the language part easy, I enjoyed the analysis of the period as a whole - studying the various styles of governance, the type of law, the differences and similarities of life now compared to thousands of years ago. One of my A level texts was Cicero's In Catalinam and it certainly is a good price of rhetoric but I always remember the discussion with my Latin teacher around it "so Cicero was arguing to sentence this person who was sort of trying to improve the lot of the plebians - that doesn't seem very egalitarian'. I think that made me a more rounded person, and whilst you could gain that experience from other humanity subjects such as English literature or history, I think the combination of the pure study of language with the contextual element makes Latin a very helpful subject to study, as it possibly comes closest to being a critical thinking course. However, I'd be happy with a pure critical thinking course being taught instead.