You've seen anglers using these on cloudy days? Maybe they think the getup makes them invisible to the fish? Like a little kid that thinks hiding under a blanket means that you can't see them.
With that said, I haven't gone to the masked bandit look yet, but I like to think I've wised up a little when it comes to sun protection. I wear those long-sleeve fishing shirts all the time now in the summer and I've switched to a broad brimmed hat on those really hot days.
As silly as they look, I think face protection would be essential if you're anywhere in the tropics is the spring, summer, or fall. The freaking sun must be absolutely searing and with the light reflection off the water, you'd be getting burned in places that were best left unburned unless you were covered up from every angle.

Better grab the sunscreen if you want to take a pee over the side of the boat!
I've heard of mountaineers getting sunburn on the insides of their mouths from the reflection off of snow. It's not much of a stretch to think that kind of thing could happen from reflection off of water as well.
Grouse