Rei actually does not need glasses. I think he wears them as a shield (my thoughts) But if you have read the novel Back Stage - I think - that is where it states that his vision is fine. (maybe he thinks the glasses make him look more mature or dependable??)
There was a short about it. It's cause Rei is too beautiful, that without his glasses he's constantly being hounded by recruiters from agencies. While Rei is content just working for Sena & has no interest in being a celeb. Also in that same short, Shogo breaks Rei glasses & after spending the day with Rei (minus his glasses) & seeing the kind of attention he gets, Shogo orders him to ALWAYS wear his glasses even though he doesn't really need them. His vision is actually way above perfect.
In one of the bonus! Chapters (Back Stage) Rei's glasses get broken and he admits that he doesn't need them. They just help repel people from flirting with him all the time which he finds bothersome.
I wonder why Rei in Shougos body is wearing glasses. Since he has now Shougos body he doesn't need them anymore, does he?
Well, it could also be because Shougos eyes are also bad but that would be... :/ bit boring