>

When you scrunch it up, you get lots of creases in the paper which adds more surface area and structural support.   
Picture a puddle on the ground: If you lay a sheet of paper down on top of the puddle, the sheet will get soaked. If you touch the sheet, your hand will get wet. You would have to pile up several sheets to get to the point where you're not risking getting  your hand wet. Even then, it might soak through or the paper might tear and then you're screwed; after all, even with many sheets piled up, your hand is still only a few mm away from the water.   
Or instead, crumple a ball of paper and drop it right in the centre of the puddle. You can now safely grab the top of the ball of paper and drag it around in the puddle. You're hand stays perfectly dry, and there is considerable distance between your hand and the water. Do this multiple times with the same amount of paper you used in the first scenario, and you've absorbed the whole puddle now with less risk of getting your hand wet. You can press as hard as you want, with less risk of a tear putting you in danger.    
Also, consider that there might be some solid dirt stuck to the floor at the bottom of the puddle.  Dragging a smooth sheet of paper across the dirt isn't going to clean it well. Dragging the rough ball of paper across it will scrape it off much better.
I suggest you further divide category 2 into 2 subcategories:
2a: People who scrunch up a wad held in the hand.
2b: People who wrap paper around their hand, entirely enveloping their hand within a scrunched quantity of paper. >

I refuse to believe 2b exists. no way >

I wasnt aware that 2a exist until this post. But i had seen idubbbz's kickstarter crap video about toilet paper "gloves". (link)