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I often export photos several times and to different folders. It would really help if Lightroom listed what folders I had exported a photo to, and when
If all your exports are being made into a certain folder area (distinct from all the LrC imported and managed files, which I would recommend, since backup and management needs are so different for these two classes of item) - there are file activity reporting utilities available which might be able to give you a log of what files were created / overwritten and when, within that section of the file system.
There's no utility I am aware of that will track this from the Catalog end. What practical usefulness this would have, I am not sure; given the reason for and nature of each export would not be documented. Sometimes we export for web purposes, or just as a test, or for sending to a printing service, or whatever and these have different significance.
That said, some sort of status flag on each image thumbnail within the Catalog (including virtual copies) showing whether that image version has ever been exported FROM (or not); also, whether it has been further modified (or not) since its latest export; those things I could see as useful and would need to be handled within LrC of course.
(edit: those using Publish rather than Export already do enjoy some of that functionality; but it would also be useful e.g. in a Smart Collection membership rule, or view filter)