It can be quite difficult to maintain a stock of consumable items like diapers because of the ever-present desire to consume them! I would suggest: Buy by the case. Take one pack out of each case as it arrives, and put it somewhere other than your normal diaper storage, that's clean and dry and can have diapers left untouched for a while. Never, ever use diapers from that location. When the stash has built up to the size of the area that you want to display it, put it on display, and make your new task to keep every square inch of wall hidden by diapers. That is easier than maintaining and growing an arbitrary size pile.
Personally, I wouldn't unpack so many diapers at once as in those pics, as I like to keep them as well sealed from dust etc as possible. However the closet does look fun, and I suppose if it is kept very clean and the diapers are used in rotation it's not a big deal.