I is well posh. I did Latin for five years (and some Ancient Greek). I have an O'Level in it.
It helped me enormously when I went to Cambridge, because I could more or less understand most of the honorary degree speeches, as well as the stuff the Parelector says when you graduate, aka "Presento tibi, Pro Vice Chancellor, hic studenta qui studiat very hard per degree course in Facultatia Educationa and learnt multa disciplinia" - that kind of thing.
I am also terribly proud of being able to understand terms bandied about, such as "In statu pupillari" and so on.
I can read stuff on graves.
I can read newspapers in Spanish and Italian, even though I never really learnt those languages. I can understand medical terms fairly easily.
I think it makes me appear posh, cultured and part of a classical education mafia. Do I think it is an automatic ticket to logical thinking and career success? No, because my mate who studied it at Cambridge ended up in a dead end job in a wine shop she hated. Do I think it's worth teaching school? It's part of our heritage, so it makes sense for kids to have some acquaintance with it, but it ain't going to reconfigure your brain any time soon, seriously. If you want that, you're probably better off learning to play a musical instrument, evidence suggests.
The Tobemeister needs to read a few books on Education, methinks, and not polemical ones his mates have written either.