I actually got into this same debate with an x last season. I'm always wear my board shorts over my wetsuit bottom. I really have no good reason for this other then when working as a guide back in PA it made you look less like a customer. I also use the pocket in my board shorts to hold my truck key and a clif bar typically.
As for the x I refereed to. She had nothing to carry, and got a kick out of how ridiculous she looked without the board shorts. Like as stated above, I quickly ended the debate because my lady was getting on the water with me. That trumped all. Unfortunately, I didn't end up keeping around for future trips. Maybe the next one...