Just goes to show what I sheltered life we live here in southern Ontario...never even heard of that (eating shrimp shells), so sure enough, I googled it and found a number of articles promoting it (also found some articles on how they can make bio-degradable plastic from them)
If I'm doing garlic fried shrimp, I'll remove the shells in advance and save them to make shrimp stock from.
My favourite mode to eat shrimp has been the BBQ though - dust the moistened shells with white, black and cayenne peppers and grill until they're just perfectly done. (and I put a pinch of cayenne in my garlic butter) Because you absolutely must try to get as much garlic butter on them as possible prior to consuming. I always tell everyone not to lick their fingers (due to the peppers) as they're peeling their shrimp, but you always do...
The shrimp we normally have outside of Toronto are just the ironically named "jumbo" shrimp which are no bigger around than my pinkie finger, frozen in the grocery stores. To get the wonderful, scampi sized shrimp, you'd need to go to a very good fish store, or the St. Lawrence market in Toronto.
I just always thought of the shells as something akin to finger nails....I mean you could, but why?
But, the one article over on epicurious, where they're recommending dusting them with seasoning and flour and deep frying them, to get that crunch from the shell - it does make you wonder if you couldn't produce something unique yet vaguely similar with sous vide and the bag being full of olive oil or butter (clarified or otherwise).
@john.jcb - you could use kitchen shears or your chef's knife to split the back of the shrimp pre-cook to get that vein out, so you needn't do so after the cook.