Japanese shops do not care about the original box simply because the box itself is important. The bigger issue is whether the item can be returned in something close to the condition in which it was sold.
That is why a return may become difficult even when the product itself is clean and undamaged. The box, manual, cables, and small accessories can all matter. From the buyer’s side, being refused a return after losing one of those items may feel understandable. If you are returning what you bought, returning only the main product can feel incomplete.
For the shop, the packaging and accessories also help show whether the item is still in a condition that can be resold. A product may work perfectly, but if the box is badly damaged or parts and instructions are missing, reselling it becomes more difficult. The packaging is therefore not just something around the product. It can be part of how the shop judges how close the returned item is to its original condition.
There is also a customer-side habit behind this. When people decide to return something, many will try to put everything back together and bring it back as close as possible to the way they received it. They are not necessarily doing this only because a store rule tells them to. Returning the whole set simply feels more appropriate. A box that seemed disposable when the product was opened can suddenly become very important once a return is involved.
Opening the box does not automatically make a return impossible everywhere in Japan. An opened but unused item with all of its packaging and accessories may be accepted by one shop and refused by another. The product category and the store’s own policy matter.
The reason for the return matters too. When a customer simply wants to return an item, being asked to bring it back in near-original condition does not seem unreasonable. If the product was defective from the start, expectations change. Even without the box, many customers would still expect the shop to offer some kind of response.