Implementing this “clean slate” command wouldn’t achieve your goal. When you as admin delete one or all messages this change will affect only new users (or existing users who reload page). Deleted message will not disappear from other users chat history until they reload page. Reasons for this have technical nature. I could complicate design to circumvent this technical limitation but this would up performance requirements and chat applications like Quick Chat need a lot of server power as is. It just doesn’t pay off to go into this.
As always, if this is something really important to you, I can be hired to implement it. I don’t believe all users would agree to up performance requirements for everyone with feature that only some users would find useful or necessary.