I’ve stored dvds in cakeboxes for long periods of time with no ill effects. Unless you are using hub printable disks, you should have a stacking ring on each disk that keeps the disks from touching one another anywhere else while in a cakebox.
Over extended periods of time, it may be possible for disks to warp slightly when stored in cakeboxes, as gravity slowly bends them. I’ve never seen it happen, but in theory this is possible.
Cakeboxes are not very convenient however. Inevitably, the one disk you are looking for will be at the bottom of the cakebox.