It's more about control and decorum than anything. By keeping a coach in the coaching box, it allows the official to exert control over situations that may get out of hand. It also forces the coach to show proper respect and authority to the official.
Also, I don't think it's appropriate for a coach to walk across the court for anything other than to check on an injured player. There's simply no reason for him to be there, especially to ask questions or to complain. I'm not sure if it's still the same in the NCAA, but I remember a time where any coach that walked onto the court to complain to an official got an automatic tech. That isn't a bad rule.
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