Why do skinny tires require less pedal effort?
Your opening claim:


  Everyone knows (citation needed) that (at fixed rim diameter) tyres with smaller section require less effort to move around (at least on a paved road).


Is actually not true. Your next claim isn't true either. The contact patch area for a tire will be nearly the same regardless of what width tire is used, for a given pressure. If I have a tire that is pumped up to 100psi, and the bike and me weigh 200lbs, the contact patch between both wheels will be nearly 2 square inches. Pressure is force divided by area. 

Your third claim is also not true, as static friction is roughly proportional only to the normal force, and it doesn't even matter, as when the contact patch is touching the ground, it's not even moving!

By varying the width of the tire, while the contact area stays constant, the shape is different, notably the patch gets shorter as the tire gets wider. This translates to less vertical displacement of the rubber in the tire as the wheel rolls. Ross Millikans answer describes, the deflection in rubber is the primary source of tire-related rolling resistance.

It turns out, that for fixed pressure, wider tires have less rolling resistance than narrow tires.

The key element isn't the width of the tire, it's the higher pressure. It is much easier to make a small high-pressure tire than a wide one, for reasonable weights and costs. Furthermore, because making a high-pressure wide tire is more challenging, it may require measures such as thicker treads that increase the energy cost of tire deflections such that it is a net negative over more deflection of software rubber, and so on.

I'm not even going to address your torque theory because you are obviously confused as to the forces at play.