I think, theoretically, a wet road will be faster. Although much of rolling resistance is attributed to the deformation of the object rolling (tire), the coefficient of friction between the two objects plays a role.

If you're not a physicist, or it's been a while since you've taken physics: To conceptualize this, imagine rolling a roll of regular tape, vs a roll of double sided tape across the floor. The tackyness of the double sided tape should slow it down first. On a molecular level, this happens between all objects, which lends to friction.

Smoothness probably plays a part, but I think that the reason you're faster on painted stripes is because the coefficient of friction is less between rubber and the paint, than rubber and tarmac/asphalt.

When things get wet, generally, their coefficient of friction drops. This is why wet roads are slicker, and why wet painted lines are super slick. So, you will be able to go faster, due to the less friction between the tire and the road, but by the same principle, why you have to take corners easier.

Now, that was theoretical, assuming the road is perfectly moistened, with no extra water to have to plow through, or go flinging off your tire. In practice, moving that extra water around will require some energy, but I don't know where to begin guesstimating whether that will require more or less energy than saved from the wet road.

If I had to guess, I'd imagine that the main reason riding in rain is slower is because of the loss of morale, and added caution when riding in wet/rainy conditions.