I can't imagine that being a good idea -- people form friendships in the office, or they just need to have a private conversation -- it seems like it would be weird and draconian to forbid that kind of thing because something important might be in a private chat.
Ah, I meant forbidding them in the sense that the culture of the organization would discourage people from talking about work related things in a "work context" via ad-hoc messages, not that people literally or practically wouldn't be allowed to message each other. I agree, that would be draconian.
