Curved Papers solves the classic RYO problem:
with square papers, if you don't keep your top and bottom edge parallel, your front corner doesn't tuck.
That's what makes it tricky to roll one. That's why you're always having to fiddle around with the corners of traditional rectangular rolling papers, and why putting one of those papers into a single-cigarette rolling machine is so difficult.
In the 1970's, cut-corners were introduced to solve this problem, they gave you some tolerance for not having your edges perfectly, parallel, but they were funny-looking and initially, nobody liked them. Nobody explained them. Elegant Curved Papers are an innovative improvement, functionally and visually. Many times easier than cut-corners, you just roll straight up the middle every time