Take a book, put it on the table, and move it. Now apply a downward force, and the static friction force that must be overcome to move the book increases.
The parallel is what happens on the faces of the lugs, provided you don't overpower the wheel and spin it out, (which puts things into the realm of kinetic friction rather than static friction). With some power on the wheel, the knobs/tread are actually engaged in the plane that is ~90 degrees to the surface of the tire. It's slight, but it is there. As soon as you apply more power than the tire can apply to the ground (i.e. spin/slide) the friction at that interface is kinetic.
The bigger benefit to pedaling through the corners is stability and the time integral of force, i.e. getting more power though to the wheels for a given time, i.e. a high average speed.