I'll second the use of simi slick to slick tread patterns for road and hardpack. One aspect of deep tread/knobs when on the road is that stuff can get trapped and "picked up" inside the tread depth or between the knobs. My Panaracer Paselas in 32mm wide pick up the tiny flecks of rock dust all the time on my touring bike. This trapping of the derbies will let them slowly have the chance to start to cut into the actual tread cap, ending up with tubes getting cut. On a trail or dirt road this is less the problem than if on the road and that derby bit is a shard of metal or chunk of bottle glass.
I have used two examples in how I describe the function of tread on a bicycle tire to my customers. #1 is using my hand. I place it on the counter top, flat against it. I then try to slide it along the surface. Like this.
Then I lift my palm off the surface but maintain fingertip contact and repeat the attempt to slide the hand. I tell my customer to note both that it's easier to move the finger tip only contact than the full hand one. I also tell them to watch my fingers as the cock/slant/lean with the tips wanting to stay put but the palm moving at their other ends. Like this:

I also tell them that if the surface was deformable (snow, mud, sand) my extended fingers would provide more traction as they were able to engage the surface and act like cog teeth digging in.
Method #2 is to ask them about their car's tires, which is about the most many lay riders know about any kind of tire (so car tires MUST be what all tires do)(satire...) I ask them if they drive with snow tires all the time, why if a deeply treaded tire is better in the winter snow/mud they are not used all year? I'll go further and describe car tires as being squeegees running down the road's surface. If wet enough the wall of water that builds up in front of the tire/squeegee, can lift it off the road (hydroplane). So tread grooves provide paths for the water to take to exit from under the contact patch. On the other hand bicycle tires take on a contact patch shape much like sailboat, with a very good water shedding around the contact patch ability, so bike tire tread is of vastly less ability to hydroplane, even if we could ride as fast as a car can go. Andy.