It is a long, long time since I had Latin lessons foisted upon me, in common with thousands of my generation in grammar schools throughout the country. I didn't know then the official reasons for Latin to be included in the curriculum and equally I don't know now what current proponents of the study of this language would say. But I did develop my own opinions, which are these.
The general effect of learning Latin was that it helped to train the mind. There were rules to be learned and applied, structures and ideas to be absorbed, facts to be understood and remembered. There was an intellectual discipline about the whole thing. Perhaps in this it was a bit like maths. I didn't enjoy it much - it was difficult and hard work, but then perhaps that was the point.
And in learning all this, a glimmer of understanding started to develop as to how European languages, not least our own, work. The structure of sentences and the function of individual words within them; much as we have within today's English but now largely hidden and barely understood (e.g. the difference between the "me" in "he gave me a book" and "he hit me with it"; or why "he likes you and me" is correct and "he likes you and I" isn't). This can all be drummed into children in English lessons but it's so much more obvious if you have a bit of Latin (or German).
As has been mentioned, English is littered with words which have evolved from Latin. A few of the borrowings are direct but the vast majority come via Norman French, the language of the educated elite after 1066. Every single word in this Latin inscription has links to modern English:
Urbs - town - urban, urbane, suburb
Mille - one thousand - millimetre, millennium and dozens of others
Artificiorum - created objects - article, artifice, artificial, artefact
Sufficient almost to work out its meaning even if you know nothing of Latin.
I won't comment on the thinking behind the use of a dead language in the middle of a city few of whose population have ever been taught it (but I should be interested to know). It might seem a bit daft. But I suppose you could argue that the words are deliberately less than immediately accessible; and therefore require a bit of effort from enquiring minds to find out what it is all about. Should suit all of us - who surely wouldn't be here in this Forum if we didn't have brains which work in that sort of way!
Chris