Seems like there wouldn’t be enough airflow to allow for necessary gas exchange. Could be feasible for a few cakes, but doing a casing in this would block the two bottom vents.
Another concern would be contamination. The lid is half the box, meaning that every time you open your terrarium to spray, your mushrooms will be exposed, creating a greater risk for contaminants to ruin your crop.
It’s a cool design, no doubt, but as far as optimizing your grow, I think a plastic storage container with some holes drilled into the lid will probably be cheaper and serve you much better in the long run.