I gave that up a long time ago, I just go ahead and wad them up because that's what they would look like after I folded them anyway.
When changing diapers the thought crossed my mind a few times that it would be a lot easier to just trade in the baby for a clean one.
Hahahaha!
You are really onto something. There's a billion-dollar business in this. I can just see a delivery truck pulling up at your place six times a day. The driver brings the new, clean baby to your doorstep and carries off the old dirty one, and tosses it into a bin in the back of the truck for processing at the factory.
One day, when enough men have changed enough diapers or enough women have gone through engineering or architecture schools, there will be special "baby sinks" in family houses that feature a molded baby-holder in a safety sink, a reliable water-temperature controller, and a sprayer like the one at the kitchen sink, so you can spray the poopy bottom with tepid water and avoid the wiping and mess. The waste and water will drain into a flushable tank like a garbage disposal without the blades, and there will also be a disinfecting function, a rediapering surface next to the sink, and a dirty diaper receptacle with consumer choices for trash-compacter style (for disposable dipes) or soaker style (for cloth dipes).