I agree with all the reasons to keep the boxes. But who here believes that if you were gone, anyone else would be able to match figues and empty boxes? I recently started to keep the boxes of airplane models, but not sure it makes any difference. The only person that could have helped my wife sort out all my stuff, was her brother who basically shared most of my hobbies. I always told her, he could help her out. We lost him to cancer in January, so there is no one that could decipher the madness. In the end I enjoy all my hobbies and when I'm gone, somehow everything will be sorted out, with or without boxes...
It may be too late for most of your collection, but going forward you could print out a small picture of the figure and slip it into the box before it goes into storage. I try to use the manufacturers publicity pics. I found that, as time goes by, it can be difficult to find references to product numbers for some of the older sets from various manufacturers.