I don't agree that what you propose is less complicated. Deriving an UV mapping along the curve could be done, but for a cubic bezier spline is not exactly as trivial as you paint it. For an example implementation along a quadratic bezier spline, see https://www.shadertoy.com/view/NltBRB. A cubic bezier is more complex to map since you have to solve an equation of 5th degree. I also think that the author wants to keep everything in vector format to be able to draw the results with a plotter. You could displace the vertices of a straight vector model of the rope using the UVs, but I am not sure that it would be any simpler.