SS on any firearm is just a little easier to maintain. And only a little easier at that. Honestly, the difference is minor. I've never seen the metal parts of a firearm rust to the point where the gun was non-functional. It could happen, but it would take a looooong time and would have to be due to neglect, SS wouldn't help.
It is the wood stock that is the weak link. I've seen wood stocks on firearms go from perfect condition to useless in a matter of minutes and the gun owner has no control over it. Shotgun owners have been much quicker to adopt synthetic stocks on guns meant for waterfowl and turkey hunting than rifle hunters. And you see a lot more shotguns coated in a camo finish. When was the last time you saw a factory big game rifle with camo on the stock and metal surfaces?
Many hunters are also concerned that the SS finish will spook game. Most big game animals don't see colors the same way humans do and a SS rifle will be much less visible to them. And considering most big game hunters are wearing orange clothing to be seen easier it just doesn't make as much sense to try to hide the rifle. Waterfowl and turkey however see colors exactly the same way humans do, and their vision is much better. Wearing camo, even on the firearm just makes more sense.
I think a combination of the above is why SS has been accepted on rifles and handguns and not on shotguns. And the trend even with those guns is moving away from uncoated SS. The various gun coatings today are becoming more popular and some guns made with SS are getting the darker coatings over the SS.
