I thought I show you the new strawberry plant box I built today for my grandson. He has strawberry plants growing the last couple years in flower bed boxes and they needed more room for expansion. It's not as thick as yours but it's strawberries and not potatoes. I did it just the way you described except for the legs as 4x4's are rather expensive. I have some in the basement but I am saving them for a bigger project. At first I was just going to use some blocks of wood to keep it lifted off the ground then decided instead to raid my grand kids box of stackable blocks they love to play with then attached with some screws then nails. Hopefully this will last him a couple years. It was rather inexpensive since I already had the wire I just had to buy the boards and the burlap.

It's sitting over an area in my yard where a house use to be, there's a lot of the concrete structure left under the dirt in that area so it's a hit and miss to use for just about anything but grass or a scattered wild flower bed. Next up is one for the pumpkins he's started, that one will sit over a grassy area where they can expand all over the place.