I have no idea what made him think of this, but a fellow named John Heisz decided to remove his table saw blade, and replace it with a circle he cut out of paper. Here's what happened:
While you can see the burn marks in the video, what you can't see is the cut quality on the successfully-cut pieces. It's shockingly smooth:
On his blog, Heisz reveals that those of you ready to try this will need some patience. "There are sections of the video where I'm cutting that are sped up as much as 16 times," he writes, "so it's not the fastest way to make a cut!"
He also tried it out on aluminum, but found that "it more or less just polished the edge before wearing out. The abrasiveness of the paper works well on wood, but is no match for anything harder."