I used this service before it rolled out widely and these boxes were a mixed bag. On one hand they worked really well, they were essentially insulated hard totes with styrofoam lining and often had dry ice in them for anything that needed to be kept cold. On the other hand, I lived in an apartment, so storing 3-4 totes for a week or more was a real chore.
The funniest thing I remember though is that the totes weren't optimized for the size of some of the products available very well - if you put a frozen pizza in it, it sat diagonally, and without enough room to really put anything above or below it. You order four frozen pizzas, and you're allocating many cubic meters of apartment space for them until the next time you order.
They must have been using different crates for you (different region or perhaps era). For me they were standard plastic bins[1] with a separate “cold bag” inside for frozen stuff. No actual styrofoam I recall, although this was also over 10 years ago so I could be misremembering.
[1] https://www.uline.com/Product/Detail/S-9745G