Noah Smith, an economist who also happens to be a nerd, made a very pointedly observation which has a lot of water to it:
What Westeros needs, more than anything, is universal literacy. The maesters and septons are holding the continent back. @mattyglesias
— Noah Smith (@Noahpinion) 3. Juni 2013
And that leads to the main problem: books are pretty expensive in Westeros, and there is no such thing as public libraries. So even if the peasants would be able to read, what exactly would they read? I'd say, however, that spreading literacy would create demand, and that demand could lead to innovation regarding the printing press. Westeros should at least start to teach all knights and lords, because a terrifying amount of them is horribly uneducated.