Set the default output filename on clips to be the original filename with suffix showing start and end time of cut. It would jsut be a default and user could accept, modify, or replace it. It could be an option in Output preferences, off by default, to maintain backwards compatibility.
Example: myvideo.MP4 >> myvideo-00.00.25.333-00.00.47.316.MP4
This would save a lot of user time in renaming files, prevent accidentally overwriting original files, and make it apparent from where in the original video the clip was derived. Another video cutter - LossLessCut (which has keyframe issues and thus not viable) - does this and in my trials of that product I found it so useful that I plan to use this naming in whatever products I eventually use.
I was just about to suggest the same :-)
IMHO a complete non-starter as export may be preceeded by multiple editing steps like pasting the internal clipboard contents and deletions.
This very specific task for including the range of export into output file name might be doable via a tinyPy script, but not completely sure.