Four things, and it is a short list on purpose. Format tracking, so a tool changing its layout is our problem rather than the reason your archive quietly stopped containing anything. Correlation, so the prompt, the response and the file diff arrive as one record instead of three directories you would have to join by timestamp. A shared timeline, so the record can be read by someone other than its author. And visibility, so 'is this working' is a screen rather than a hope.
Notice what is not on that list: we do not capture anything the script could not, in principle, copy. The data is the same data, written by the same tools, to the same disks. Anyone claiming a fundamental capability difference here would be overselling.