First off, Jesus wasn't illiterate. The gospels recall several occasions in which he read scripture to various people.
I believe that the best way to answer this question is to consider the purpose of Jesus's teachings. Jesus, at one time, refused to help a Samaritan woman, telling her that he was sent only for the lost sheep of Israel. At the time of his ministry, he encouraged the Jews to keep God's law and Jewish festivals and traditions. Also, he almost never traveled outside of Israel, or preached to non-Jews.
It wasn't until after his death and resurrection that Christianity was founded. It was then that he told his apostles to go forth and make disciples of all of the people of the earth. Before that, Jesus and his apostles were all practicing Jews, and Jesus's ransom sacrifice had not yet been made.
In fact, it was necessary that Jesus be a good Jew in order that he could die as a sinless man. And without the ransom sacrifice, the Christian hope of resurrection as brothers of Christ would not have been possible, so it was not until much later, when the apostles were preaching to large numbers of non-Jews that the gospels were needed.
Even then, the teachings of the gospels were much different from the message that Jesus preached himself. Instead of telling people to be good Jews, the apostles were teaching them to be good Christians.
But regardless, the writers of the gospels were, for the most part, eyewitnesses to the events they described, and even though there may be minor variations in the way they described accounts, they do not differ at all in their message. So I don't believe that is was necessary for Jesus to have written the gospels himself, and if he had, they might not have survived long enough to be useful to the first century Christians anyway.