Having only tiny loft space, an already full garage, and shed intended for other things, I keep only boxes that I think I will need, whether hi-fi, or anything else. Buying most hi-fi gear secondhand, often not having manufacturers’ boxes, minimises boxes! The smaller boxes, I do keep in the tiny bit of loft. Both my last speakers and current ones that I bought only six months ago came in the original boxes, which I have kept. With the speakers being relatively large floorstanders, they are big boxes! I collapsed them and put in the shed, the flattened cardboard against the wall, and the packing pieces/spacers bundled together as best I could, wrapped tightly with plastic to hold together, and also in the shed. Not ideal as still occupies space, but if I were to move house, let alone sell the speakers, they would be invaluable for protecting them. (Last time I moved house with large speakers, without boxes, I had to build something to protect them while manhandled in transit.
Keep them all as a rule but … In house 1 … I kept ALL the DBL boxes and when the time came … back in to their boxes they went, and off to house 2. In House 2 … Oh, I tried, I really tried, trust me … but have you seen these things? The Base boxes had to go in the outside shed where sadly they disintegrated a few years later. But to the eventual new buyer I could at least offer ALL the foam packing, plus the boxes for the bass units and HF/MF units. And guess what … they wouldn’t fit in his vehicle, so it was, stuff it mate, just help me load the speakers in, we’re fine