Q:

Why does the friction force on a smoothly rolling wheel cause the centre of mass to accelerate?

Suppose you have a wheel of mass $m$ rolling down an incline. Then the component of the weight along the incline acts on the centre of mass of the wheel, causing it to accelerate. The (static) friction force points up the incline. This friction force acts on the point of the wheel that is in contact with the incline and therefore a torque causes an angular acceleration, i.e. the wheel rotates while rolling down.
I have read that this friction force acts on the centre of mass of the wheel, too, causing the centre of mass of the wheel to accelerate more slowly than a block on a frictionless incline.
I don't understand how the friction force is transmitted from the bottom of the wheel to the centre of mass. I can only see that it acts as a torque on the bottom of the wheel, thus causing rotation. (I mean, a force cannot act on two different points at the same time, right?)

A:

I don't understand how the friction force is transmitted from the bottom of the wheel to the centre of mass.

It's because the wheel is rigid and forces at any point on the object are distributed through to other portions of the object.
For linear momentum problems on rigid bodies, $F_{net} = ma$.  The location where the force is applied does not matter.
The force does not act at two different points, but it can certainly have two different effects (changing the linear momentum of the object and simultaneously applying a torque to the object).

