I suppose you could try to think of the problem in another way.
What would happen to a cylinder (or sphere) if you put it on a frictionless inclined plane? Would it still roll or just slide?
The imbalance in forces acting on the cylinder at different points, with respect to its center of mass, are what lead to the rotation. Gravity acts on the center of mass while friction is acting at some distance, R, from the center of mass.
Here is another fun thought experiment. Suppose you have a cylinder of radius R and length L. Now at its center of mass (i.e., at L/2) imagine it is incredibly thin (i.e., r $\ll$ R) for a very small length (i.e., $\Delta$l $\ll$ L). Put this cylinder on a thin rod of the same diameter as $\Delta$l.
Now, would the cylinder roll or slide?
Let's cheat and imagine r to be infinitesimally thin so as to be effectively at the objects center of mass. Then ask the above question to yourself again.