Well, since God does not answer us directly, and answers our prayers to do so only through his moving in mysterious ways programme, it is impossible to answer your question.
Still, we can guess. And that's what any theologian does for a living. Makes guesses and presents them as infallible facts.
Some people say Mohammad was not and could not be illiterate. He was the son of prominent aristocracy in Mecca, he was in trades business which at least compels you to learn aritmetics, which requires knowledge of written symbols.
Besides Mohammad is considered an intelligent and curious person, it is quite improbable for a person of his grade to be ignorant of letters in the *then* cosmopolite cultural atmosphere of Mecca.
Furthermore some people consider the word ummi does not mean illiterate, but a person who have not read other holy books (old and new testament) in existence. This one I think is plausible. Because Mohammad is usually mocked by others as an impostor who copies "the ways of the old" and its texts. So it is only natural for Mohammad to call himself ummi, a person who does not know about these books, so he can not possibly copy them for his purposes.
Eventually since Islam needed a miracle and had to suppress this obvious connection, invented "the illiterate prophet, who by the sheer will of Allah learns to read and write" story. It caught on.
It even sound very convincing when you think of Koran as a piece of literature. How can an illiterate man write this beauty? Obviously it is the word of god, etc.
However Koran is a very disconnected book, that can hardly stick to a point, full of redundant terms and meaningless drivel. It's very easy to imitate, and even a poet during Mohammad's time imitated one book that reads like Koran as an answer to the challenge, only to be executed for doing so. It quickly killed away the opposition, leaving true believers who can not praise the book more.
Anyhow, ın short we can say: even if Allah picked Mohammad, an illiterate man to be a prophet, it's not strange. Many people believe without reading, an illiterate prophet won't hurt sales that much.