I've wondered exactly this myself, and tbh I don't know enough about the science and metallurgy of what's going on to be able to answer it satisfactorily. Because you're right; bevel geometry shouldn't make a difference, paper towel falls away as you cut it, it's not a carrot, you can't wedge in paper towel. Given two otherwise identical knives, one thicker one thinner, but sharpened at the same angle in the same way - they should also cut paper in the same way (afaics).
But all of my lived experience says that bevel geometry does make a difference. That Sab didn't do that before my latest round of thinning, even when finished on a Coti or Washita, let alone a King 800. And I see it at work too when sharpening other people's knives that are fat bte. At the extremes it can actually be quite difficult to get any kind of working edge onto some really thick knives.
My only possible guess as to what's happening is that if the steel is thicker leading into the edge; then perhaps burrs and edges actually form in a different way compared to a knife that is properly thin leading into the edge(?). That's pure conjecture, but it's the only reason I can think of to explain it.