There is a difference between not paying attention and not registering memories. Millions of people operate cars a little zoned out every day. With both hands on the wheel and a decent level of experience, your muscle memory and natural reactions will operate the vehicle adequately.
Zoning out a little on the road does not equal distracted driving like text messaging, loud kids, or fiddling with screen controls. Your mind is still focused on the task, even if you aren’t registering memories about it.