Well . . . you're not going to cross-fire with a pump or auto, for sure. But does that guarantee the gun shoots where you aim it? If we assume that the barrel is perfectly straight on a pump, auto, or single barrel, then why do we bother checking where a rifle shoots? After all, the spread of a shotgun pattern is going to compensate for some degree of impact error. In other words, while you may miss (or just chip) a target or a bird you should have hit had it been just right, you'll also hit some you shouldn't have hit had it patterned dead center. You don't have that same margin of error with a rifle, but you still check.
The only problem a double can have that a single barreled shotgun can't have is cross firing.
A single barreled gun is infinitely easier to get to shoot where you are looking than are two barrels, joined together, that are not properly regulated. You can make several changes to the single barrel to get it right, not so with a non-regulated double. You can get one barrel right, easily, but how about the other? The idea that you will hit some birds with a non-regulated gun, that you wouldn't with a properly regulated one, is true, but is so alien to my way of thinking that I can't assign it any import. Why make allowance for misplaced impact? I just cannot get my head around that. To me, it's like the guy whose pickup pulls badly to the right, and he has to drive with both hands applying pressure to the steering wheel to keep it straight on the road. When asked why he doesn't have it corrected he says, "Well, it takes a right curve in the road beautifully!".

No man alive can do his best shooting if he knows, in the back of his mind, that his gun is inferior. And, IMO, a non-regulated gun is inferior.
I also disagree that the only problem a double can have, that a single barreled shotgun can't have, is cross firing.
Any misplaced impact that causes the barrels not to print their patterns on top of each other is a problem unique to doubles. They do not have to be cross firing, they can be doing the opposite. Or, as is it the case with an O/U I saw patterned, one barrel can be shooting to the POA while the other is off half a pattern or more.
All reasons why, for me, lack of regulation is the biggest issue facing a double gun buyer.
SRH