Could someone give me an example of where it would be advantageous to use the Take Command "Command Input" window, rather than just use the TCC command line? Is there anything I can do in the "Command Input" window that I can't do just as well in TCC?
The command input window was originally added for accessibility support (for example, for blind users). It also had some features that weren't available at the TCC command line, but almost everything is now also in TCC.
So unless you need the accessibility features (or you want to send input from a single command input window to multiple tab windows) there's no reason for you to use the command input window.
I always thought it was there to add history and completion features to other console-based programs. If you used some other app that didn't support, say, file completion, the command input window would be helpful. I don't know why anybody would use such an app, but then I don't understand a lot of what people do.