I always do. I sometimes wonder why I do it. I think it's just a habit I picked up early on that never really did me wrong. But I have had problems with wicking when I got lazy and didn't peel before cutting. I've always done it that way, so I'm geared towards always doing it that way, and with that comes certain expectations, which may in fact, be completely imagined, along with the perceived results. I've never given it any thought before.
I think it really all comes down to your wicking technique. Personally, I think the outer, compressed layers of wick do me no good, so I discard them, but perhaps that only works better for me because I learned to wick with those outer layers gone. It's possible that the only thing that really changes significantly is how one estimates the appropriate amount to cut.
Sometimes, I think it's an OCD thing. In my mind, they shouldn't be there and they just have to come off. I feel anxious leaving them on. I also bite my fingernails and chew on plastic bottle cap rings impulsively, though.
I have a buddy who never peels his squares, but he seems to get similar results, even when we build the exact same coils, though our techniques for fluffing, inserting, and positioning wicks are also very different.