Road Helmets do not come with visors. MTB helmets do. Visors are not much good for anything. I wear a cycling cap under my helmet all the time. The short bill works great for sun without blocking view of the road. It acts like a helmet liner. If you are bald. It prevents you from getting sun burned spots on your head. Keeps you from looking like a newcomer on Alien Nation. It keeps sweat out of your eyes. Does the same thing for rain.
Eye protection is a must riding a bike. I have prescription riding glasses. They have a bifocal and Transition high impact lens. I have 3 pairs of them. One pair is retired after a nasty crash. The helmet saved me. The glasses saved my eye. I have nasty pics after the surgeon sewed my eyelid back on. Before my eye doctor turned me on to the Liberty Sports glasses. I used one clear and one tinted pair of cycling glasses. Walmart optical now sell the Liberty Sports Cycling frame for about 50 bucks plus your prescription.