Joke aside, to wealthy and powerful Romans of the time, many thousands, maybe tens of thousands of books and tracts would have been available, possibly even to middle class people. There were even publishing industries and trends akin to reduced versions of today's best seller phenomenon. Someone like Diocletian, Vespasian or his son Domitian wouldn't have had much trouble with interesting literature.
True enough, although most of those tracts would be dreadfully short by modern standards; the Aeneid waa around 130k words -- compared to 80k for the first Harry Potter and 485k for the fourth Stormlight Archive -- and the 8 books of Caesar's Gallic Wars were 5-15k words a pop.
Assuming ancient readers were as proficient as modern ones, "reading every book available" was a reasonable ambition back then, and you were almost certainly limited by money and availability more than time.
