In class that is good. However at lunch kids should be talking to other kids. I know many teachers/schools are control freaks and so they would do such things, but it was always evil.
Have you never been to a room full of people/children? If there aren't these 'control freaks' in the room, then it gets louder and louder until to the limit where nobody can understand anything while all are shouting. It's surprisingly fast, about ~2 minutes to the maximum/stable loudness. This 'control freaks' are the requirement to allow children to have a conversation.
Properly treated rooms make a big difference for this. When the walls are painted concrete and the ceilings are unfinished this happens almost immediately; when the walls and ceilings are acoustically treated, it's much better. (Carpet makes it even better, but I would definitely not recommend carpeting a school lunchroom).
If the teacher completely forbids talking, they will just talk right around the corner, or write on paper. They will be just unable to impose it on the children for long.
