How do treads affect traction?
If you are riding on the road, you don't need treads. Even with mud. Even with sand, or gravel. Unless you are riding on the street in the middle of a volcanic mudslide or torrential rain washing out the road, it won't matter. The curved cross section of your tires coupled with your mass will instantly cut right through any patches of water or mud as you ride through. A bicycle under human power won't "rarely" hydroplane, it will never hydroplane.

You can slide if you ride over sand or fine gravel. The gravel can get between the rubber and road, and cause you to lose traction. However, having treaded tires will not save you. The layer of sand or gravel will be just as slippery to the treads. The treads can't cut through the sand or gravel, because the underlying road cannot deform. The treaded tires will just slide along the pavement, lubricated by the sand or gravel, just like a slick.

A behavior you didn't ask about, but you can encounter, is a squirming feeling, that you get if you ride an aggressively treaded tire on the road. This won't happen riding on dirt or sand, because the ground can deform. This squirming and deformation becomes especially troubling when cornering. The sudden transition from smooth to treaded in those silly combination tires, right during a hard corner, is especially nasty.

The reason companies make treads on pure road tires, like Blam suspects, is simply because the majority of bicycling customers don't think about these things in great detail, and think that their bike is just like a car with 2 wheels, and since their car tires have tread, so should their bike tires.

The takeaway principle is that conditions that will result in a loss of traction on the road, will do so regardless whether you have treads or not. Treads reduce the consistency of your tires surface, and in doing so, makes for a worse road tire.