I was watching a video where a person made a supersaw by layering the same sound and panning it once left and once right. A center-panned sound already outputs to both left and right channels, so what's the purpose of this?
This is because one stereo separated super saw (6-9 voices) will have the same phase drift in both the speakers.
However, when layering the sound with itself and pan one to the left and one to the right, you get 2x the same sound, but each having a different phasing to them (since the phases have a factor of randomness added to them by your DAW to make them sound "nice" and "crisp"), thus creating more detail, more phasing, and with that, more depth to your sound.
I suggest looking up SeamlessR's explanation on phasing for more info.
As the question is "why would you" I'll offer another answer without covering the explanation as to why it works: if you have some vocals, for example, you can make the sound appear to come from both speakers instead of in the centre by giving the sound on one channel the tiniest of time delays - it's enough to have the desired effect without the difference in timing being enough for the listener to sense that they are technically out of time with each other.