You could do that for the bottom if placing a box or bag inside would clear. Alternatively you could frame the bottom so it slips over the boxes outside, Then screws could be shifted slightly outward from the centerline of the sides for more "meat" on the inside for screws. Truly, if your screw pilot holes are correctly sized, they won't cause cracks in the sides.
Trick to the lid is to get your sides all mitered and glue-ready so you know exactly the size needed for the lid.
Here are some better details if you decide to try this style of lid at some point.
