Aristotle and the Exoteric Works

How wide was the knowledge of philosophical texts actually spread throughout what we're generally calling ancient cultures? Does it mean that anyone with an aristocratic upbringing would have read some Plato? Would that be going too far? I think you get a strong sense that anybody who wants to count themselves as a cultivase in person has got to be able to recognise the names and doctrines. There's a big body of material there that people are working from.