As a side note I do think Latin language should be become the official language of the EU. It's dead so - its a compromise for all member staes - you can change as you like - it was used millennials as a law language so it fits
I think that is a reason the catholic Church still uses it for things like papal encyclicals. It puts different groups on a more equal footing. Far more people understand it than things like Esperanto. Quite a lot of people know it a bit. I did it at school. My kids learned some (their choice to do it up to GCSE level). That said, in practice, English is the international language. It is what is most likely to be use…
Nah, it's just because that particular institution tries very hard to be internally consistent, for historical reasons. They immediately publish translations of such documents into "common" languages as well, and that's what non-clerics will actually read.