If you're an Anglophile, I suppose, slinging a shotgun is blasphemous. I wouldn't disagree with you if we are talking classic British style shotguns but for continental guns a sling makes a lot of sense. It is not uncommon to see shotguns slung in Germany, France, Spain, Italy among others. Since the Alps or other high mountain ranges dominate much of the terrain in some these parts it makes perfect sense to sling the gun. Of course it deters from the aesthetics but its a function over form thing.
My Merkel Model 8 is without a doubt the complete opposite of what would be considered appealing to the English form. It has a pistol grip, cheekpiece, its over engineered with locking lugs and a Greener crossbolt lock and a sling. By British definitions its gaudy, by German definitions its practical. I have climbed mountains and rocks, freeing my hands to support myself when moving. I have marched through marshes and muck so when I fell my gun didn't get buried in the mud. When hiking toward a duck blind, I can sling the gun and use my hands to carry decoys, dog stands, blind material, etc. With a break barrel, I can break the gun and hang it on a tree, branch or anything else and keep it from the mud.
I don't sling all my shotguns but on some I do. The slings I use for my Merkels are from Akah. Akah is the German equivalent to our Cabela's except they don't sell crap. They sell quality hunting goods and fine guns. I wouldn't add sling mounts to an existing shotgun if it didn't come already attached but if your gun comes with them I'd suggest putting sling on it. Even if it seems wrong.