After all, there are loads of books and literature in Eorzea! And judging by market wards, books seem to have 
some value (including history books, etc). And most people seem to be literate - ordinary citizens in Limsa reading signs, the pirates in Sastasha leaving clues on parchment, Gerolt reading books about weapon's history... Heck, the people we get challenge logs from even keep journals!
You can't tell me they're all just born with the innate ability to read - it has to be taught and learned somewhere! It may not be evidence of a school (homeschooling, for example), but it is certainly an important enough skill (if even average citizens display literacy) to warrant there would be several places of learning 
somewhere. 
Whilst we do have a lot of lore, there is so much more room to flesh out our cities in a myriad of different ways, which gets me so excited thinking about the possibilities! 
