I believe that encouraging a child to speak in class teaches them a vital life skill of being able to speak whets on your mind, this becomes very important once you enter the workforce and want to establish a presence, speaking in class also helps a child become comfortable in social settings.
The classroom should be a place where children learn that other people's needs and thoughts are no more or less important than their own. There's no better way than allowing children to speak as long as they raise their hand and it's pertinent to the subject, with the understanding that only emergencies can be blurted out. It is frustrating and dangerous for a child to be told not to speak under any circumstances because a grownup is talking. It does not increase respect for others, but makes it less likely since the child does not feel respected themselves. Teaching by example is the most effective way to teach anything from math to social and moral lessons.
More and more science is coming to the conclusion that the earlier you teach children, the better off they will be down the road. If they teach kids to speak in front of the class at a young age, then it will less traumatic for them later. They also could do some early classes on how to treat your fellow classmates. The civility issue could go along way to helping kids be more willing to speak in class.
If "speaking" in class refers to being more vocal during a class presentation, then yes, children should be encouraged to speak in class during assignments. I don't think that children should speak however in class if they have not been called on by the teacher. I think that helping kids learn speech skills is important.
Yes, children should be encouraged to speak in class, because students should be taught that their ideas and opinions are worth while. Perhaps students become shy during their teenage years because they spend so much of their time being told by teachers to sit down and be quiet. Self-expression would be a positive for students.