Wood is a wonderful engineering material! If you use MDF or OSB I can definitely see an issue, and you definitely want to ensure you've got the bed torqued near the design, but the design can work well especially as it's not permanent and the box itself is carrying very little load away from the fasteners.

The expansion of the wood will definitely cause audible pops, but if if the bolts are washerd and the plywood is a high grade I think it will work nicely.

 

Yes, wood is amazing. But its interaction with steel is NOT predictable to the degree needed for vehicles, which is why Ford stopped using it in truck beds nearly 4 decades ago. Attempting to re-introduce it now would be risky at best.

BTW
OSB would be superior to plywood in this application, but still not suitable.

 

Possibly. I'm not great with wood, metal is more my thing. Depends on the loads and fastener. Given though the bed is effectively a washer in this application, OP is presumably somewhat mechanically inclined, and the loads are relatively small compared to capacity, it's worth thinking more about (when i'm not 6 "drinks" deep) 😆