I moved last year and tossed a bunch of boxes. But those that I kept and used in the move were for my most expensive electronics and I’m glad I did. As usual, the packaging that can withstand shipping halfway around the world was a perfect match against the somewhat incompetent movers that I hired. Mistakes were made, but none of my gear was damaged.
This is the big reason. I keep the boxes to make future moves easy, learned the lesson the hard way.
Other good reasons are the box keeps all the accessories in one place while saying what they are for (psu boxes, looking at you) or the box is great at storing that type of item, like the box my NAS drives came in, perfect foam insert for other drives