I really dont believe that the Jews in the first century, or ancient isrealites were as illiterate as people assume.
Amos was a raiser of sheep, and Micah was a prophet from a rural village; yet, both wrote books of the Bible.
The mosiac law required that the isrealites 'read Gods word day and night' ... who would put such a requirement on a nation who were illiterate?
Jesus was known to read publicly from the hebrew scriptures and could readily quote them...same with the apostles who were able to refer to the Hebrew Scriptures hundreds of times in their writings.
Archeologists also found a small limestone plaque called the Gezer Calendar which dates to around the 10th century BCE. Scholars believe that it belonged to a young farm boy because its written in verse (used as a memory aid) and lists the features of the agricultural year.
So to claim that the ancient people of Isreal or the 1st century jews were mostly illiterate is quite speculative....unless of course you have some evidence which can back up the claim.
Amos and Micah may not have written the books accredited to them. That is the nature of the Bible. We know very little about who wrote the actual books. Yes, they are accredited to certain people, but for the most part, we simply don't know.
As for the mosaic law requiring people to read the scripture day and night, it really doesn't matter. In the first century C.E., buying copies of the scripture would have been quite expensive. One could only have them hand copied, which took money to do so. Under Roman occupation, we know that many Jews simply did not have many luxuries (as scrolls would have been). The reason being that they were lower class. Looking specifically at Nazareth, where Jesus was born and would have grown up, we know that they were for certain lower class. Jesus is called a tekton, or the son of a texton, which would put him very low on the social scale. He was an artisan peasant, which was lower than a farming peasant as they had no land. Basically, he was most likely equivalent to a modern day handy man. Barely surviving. They would not have had the money to buy scrolls. It just wasn't logical. And that is true for most 1st century Jews. It simply wasn't feasible.
As for Jesus reading publicly, only Luke mentions this. However his account simply is not probable. First, there was not a synagogue in Nazareth in the 1st century. The size of the town would not have even warrant one, plus, synagogues as architectural buildings did not develop until later on. Second, the verses that he supposedly read from Scripture would not have been possible to do so in the manner described because of the nature of scrolls, which were the medium of that time. Finally, there is no cliff that the towns people could have threatened to throw Jesus off unless they decided to chase him for quite a distance, and that is now what Luke says. There is no reason to believe that the verse in Luke is historically accurate.
However, they did live in an oral society. Meaning they were more apt to simply memorize different pieces. Scripture would have been something that religious figures would have memorized, the same way that they do today. It does not mean that they read the scripture though, but that they were taught it from family (who had already memorized it), or that they heard it read aloud, as was common during that time. So it is very likely that Jesus and the apostles knew scripture and had it memorized. That does not suggest they could read and write.
To go further with that though, it is for certain that the later writers added much of the scripture to the Gospels and NT by simply copying it from their sources. The thing with an oral society is that people remember the gist of what is being said. So Jesus and the apostles may not have quoted scripture 100% perfectly, but when the later writers wrote in the scripture that was supposedly uttered by Jesus or the apostles, they simply copied it from actual scripture instead of portraying what Jesus and the apostles actually said.
We know that the people who wrote the books of the New Testament could read and write. The thing though is that besides Paul (not all of the work that bears Paul's name was really written by him though), and the John who wrote Revelations (it is very likely that a John did write Revelations, we just don't know which one, and he was not closely related to Jesus or the disciples), we don't know who wrote the books of the New Testament. We know that they are accredited to people who supposedly were connected with Jesus or the disciples, but we also know that they simply were not. So besides Paul, who was not a disciple, we don't know which ones of Jesus's early followers could read and write, and we have no idea whether or not the disciples of Jesus were skilled in these areas. If they were, we have no evidence for it.
As for the literacy rates during the first century, in the Palestinian area, scholars agree that it was between 1-3%. During Roman occupation, it may have gotten to 10% at the highest, but that is leaning more towards the end of the first century, and further on that way. Here is one online source that explains it very well.
Illiteracy in the Land of Israel in the first centuries c.e.