There are several reasons why the author does that. A possible answer is that the author wanted to build up suspense. By withholding some information, and only revealing it in stages, the author hopes to interest the reader and to keep him "hooked" so that the reader continues with the work.
Another reason could be that the author wanted to mimic the way in which the characters of the play obtain information. As the reader does not know all the facts, he can emphatize with the characters, who also do not have all the information. This makes their confused state and their imperfect decisions more relatable.
To build suspense. Plays are not interesting without conflict. In this case the conflict surround John Proctor, the tragic hero, we would not be interested in Puritan drama.
