I've posted this before, but I guess it bears repeating here...
Leather is not magic. Neither is cardboard, paper, your jeans or the palms of your hands.
What they all have in common are 'silicates...' those tiny abrasive particles, MUCH smaller than 98% of what are found in various compounds, and these are the 'magic' to be had in stropping on bare surfaces.
All carbon-based lifeforms contain silicates to some degree. Green grass has a lot of silicates, and when the cows eat the grass, they now have silicates in their skin. Vegetables have silicates so when you eat them, you have silicates in your skin. Trees have silicates, and when you grind them up and make paper, the paper has silicates. Jeans are made of cotton, cotton has silicates so your jeans now have that magic micro-abrasive quality that allows us to strop on our thighs.
Leather, properly processed, has MORE silicates than cotton cloth. Especially horse hide. It has more silicates per square inch than cow hide. So does kangaroo hide. BUT NOT A LOT MORE! Just more. Without real science (and so just making up numbers,) if it takes 6-8 strokes on Horse hide, it may take 8-10 strokes on cowhide and 12 strokes on paper or on your jeans. There is no difference in the quantity of silicates in copy paper or a shirt cardboard, and it's those silicates that are doing the honing, not the smooth or rough surface of the paper/cardboard strop. Magazine covers are a horse of a different color. They are 'coated stock.' The coating is a fine clay, which is abrasive in its own right. And because leather lasts longer, barbers use leather strops rather than cardboard toilet tubes. Looks more professional, too.
Different stropping materials do give us different feedbacks while we are stropping. And we get used to the feedback of the strops that we use, so we may feel that one is 'better' than another. Rougher surfaces really have little effect when stropping, other than giving different feedbacks. The bottom line is that it is the silicates that are doing the work. If you doubt this, just try stopping on a rough piece of Cordura Nylon and see what happens. Then try stopping on your jeans or a piece of news print paper. The magic is in the silicates.