That styrofoam packing is not nearly as safe as several layers of bubble wrap, where you could in theory bounce the bottle on the floor without damage.
Back on topic: I have seldom had issues using tough cardboard boxes to ship household items. You just need to tape them up securely. Plastic storage bins with luggage belts seems a lot riskier.
Agree on plastic storage bins. Cardboard box can give a bit without the box being totally destroyed. Plastic bin gets hit and there's no give without breaking. Bag conveyor belts are not nice to bags. I've had enough hard sided bags come out damaged would never use a plastic bin.