Amazon provides the subscribe and save service to fill this need. You can set up the frequency of delivery and the quantity of units and never have to worry. They give you a nice discount on the order if you do it this way as well
Clearly you are only passingly familiar with young children. ;) As @mathattack implies, one cannot predict an infant's near-future need for diapers with the same confidence with which one can predict e.g. when a furnace filter needs changing.
The issue isn't about planning. It's, "Holy Sh*t, the baby just pooped 3 times in an hour, and I have 1 diaper to hold me until tomorrow" When that last diaper goes, instant service is at a premium.