This might be TMI but I never understood toilet paper. Think about it. You are taking a piece of paper and just spreading it around. No matter how hard you try it's still there. It's not clean. Gross. In fact, the use of toilet paper has spurred a whole new industry that most other countries don't have...the ointment industry. Washlets or bidets are far cleaner and preferred.
Seems like that same logic would obviate the dish cloth/sponge, dust cloth, mop, and towel too. Since these devices actually work, I suspect you're thesis is kinda wrong. Needless to say, when you wipe with an "clean" cloth, some of the material you want to remove sticks to the cloth and gets removed, leaving less on the surface being cleaned. Some number of repetitions pushes the concentration down below whatever it…
Let's assume you have poop on your hands, would you clean yourself with paper?