In closed countries and in countries where Christianity is in a minority, it is safer and less confrontational. People who would never stop and listen to you speak would take your literature and read it in private. This helps calm their fears and gives them an element of comfort. It is very cost effective. In proclamation evangelism it is not always practical to reach every person, so literature fills the gap.
People are very curious and want to study and understand new things.
Everyone likes free gifts. People will usually line up or even mob you to get the 'free' gift . Literature is non-threatening. Some cultures and peoples' personalities do not respond to confrontational evangelism. Some people are shy or scared to talk about their feelings but will listen if God speaks to their heart.