I don't really collect the DVDs or Blu-ray sets of anime. However, I can relate to your situation.
My collection comprises mainly of figurines, manga and some console video games. Like yourself, I keep the boxes even after the contents within has been opened. Some of these boxes, or should I call them "packaging", are wonderfully done, which I believe aids to attract potential buyers, especially the limited edition of figurines and video games.
For example, a figurine could come within a box, which has a flap. Only by opening the flap can one view the figurine within. The flap is held in place by velcro.
With regards to video games, even though more gamers are turning to digital copies, which could be cheaper and indeed saves space, I prefer physical copies. Call me old-fashioned, but I grew up with video games sold in boxes, with ultra-thick manuals. Part of the fun was reading these manuals, introducing the characters, gameplay, etc. Of course, we now have the internet for guides and walkthroughs, but physical copies continue to mesmerize myself.