I know that tread causes squirm, which increases rolling resistance by creating waste heat. I'm not sure how much effect on traction the squirm has for pavement use; but probably minimal. I always understood that traction was primarily a function of the rubber compound. It seems to me that it would take a lot of tread to make a hard rubber compound act more resilient, whereas a softer compound would be resilient on its own.

The only times that tread has much effect on traction for me is in grass, snow, or soft dirt/sand. Most of my tires are either slicks or have minimal herringbone or sipes.