Interesting. I haven't done a lot of duck hunting, but I've done a fair amount of driven shooting--where you almost always have another "gun" to one side of you; usually both sides. Not to mention beaters often in sight and coming at you, and pickers-up behind you. You're pretty darned near surrounded! Yet the guns they don't allow are pumps and autos. One reason being that it's very easy to tell if a double is safe: When it's broken open. Much harder to tell on a pump or auto. And when the birds are coming hot and heavy, also easy to forget you have a loaded shell in the chamber.
The only advantage I can see to a pump or auto in a blind is that you can load them with the barrel pointing up, while you can only load a double with the barrel pointing down. So if you've only got one guy with a double and he's right handed, put him on the left end of the blind. His natural way of loading is with the gun pointed down and to his left. No one there. Much like the procedure my hunting partner of 40+ years and I have adopted--in addition to following all other safety precautions: I'm right handed; he's left handed. I always hunt to his left. That way our guns, in normal field carry position, are always pointed away from each other.
This is smart because blinds should be set up according to the needs of a shooter. I like the Browning BPS because it ejects downward and is easy to protect its action from collecting dirt or water. It is easy to load when you are wearing gloves. They can stick BPS user anywhere. I like the old A-5 also because of the autoload feature I can slip in a steel 7 on a wounded swimmer in the water because you need a shot to bounce him on the head to stop him. Every thing else vital is below the water line and a 7 will put more shot in the air.