Question

It is well known in racing that driving the car on the ideal "slip angle" of the tire where it is crabbing slightly from the pointed direction produces more cornering speed than a lower slip angle or a higher one.

(More explanation as requested) I'm considering two main effects on the tire when in a turn:

The tread of the tire is twisted from the angle of the wheel it is mounted to. There is more force as speed increases, and generally, more twisting.

The tire slides somewhat at an angle on the road surface rather than rolling.

At low speeds, the angle between the pointed direction of the wheel (90 degrees to the axis of rotation) and the direction of travel is nearly 0. When the speed increases to the point the angle reaches about 10 degrees, the tire generate more grip and the car goes faster around the turn. (Higher angles produce lower grip)

So the grip is higher at 10 degrees of slip than at 0 or 20 degrees.

What is the physical effect that causes this increase in grip?

Answer 1

The simple answer

The tyre is deformed sideways due to the sideways force like Stingray describes, but only around the contact with the road, the rest of the tyre is not deformed so.

The tyre constantly rotates. As the contact pad is lifted off the road the force is taken off this pad and thus it undeforms, meanwhile a new part of the tyre get into contact with the road and is therefore deformed instead. A new deformation happening always moves the car a little sideways, and as new deformations have to happen as the tyre rotates this sideways motion depend on the speed of the car.
The more exact event description

My description has been stepwise, but this is of course a fluid motion. Lets consider a small part of the tyre on its way through the contact area with the road. During the contact phase the tyre part gradually deform more and more, this process must be linear, as the car is moving sideways at a certain speed any point of the tyre that is stationary relative to the road must deform at this speed. The lateral force on the tyre part increase with this deformation.

For the first part of the contact phase this actually looks like a pretty neat pattern, the vertical force increase from the start of the contact pad to the middle of it, so the same coefficient of friction can gradually support more lateral force. Unfortunately towards the back of the contact area the vertical force decreases while the lateral force continue to increase, at some point before the end of contact area the coefficient of friction can't keep up and that part of the tyre slips.
Conclusion

Part of the tyre is slipping, and thus causing degradation, disproportionately more so the close you get to the friction limit. But the grip come from the part of the tyre that is not sliding, this part is however in a constant motion of deformation that effectively makes this part of the tyre rotate in a slightly different direction than the rest of the tyre.