Yup. Both our dogs are shelter dogs and we love 'em, but in the newest dog's case--he's probably around three, we've had him for about six months--there are enough issues that a lot of people wouldn't want to deal with some people just couldn't, while still being very good caretakers of better-adjusted dogs.
In ours's case: he's not a barker and he's incredibly gentle, but he's both dumb as a post (not the shelter-dog problem, and also usually just hilarious) and extremely timid (that one is) to the point of frustration. Speak excitedly? He'll slowly sink to the floor and look worried. Tape a cable to the floor with gaff tape? He won't go over it[0]--probably because he'd experienced an invisible fence, we think. Move a chair to the other side of the living room? He sits in the corner and quietly freaks out for two hours. Leave after such a traumatic furniture adjustment? You might come home and he's nervous-chewed something. (Like, to this point, five pairs of my shoes. I am literally bankrolling Nike by my re-purchases of Air Force 1's. It doesn't help that now he's figured out how to open the doors that don't latch in our house--we're doomed, I tell you. Doomed.)
He's a great dog. But we knew going into it that dealing with his issues would take some effort, and there definitely are people who could be enriched by having a dog (they're great!) but don't have the capacity to deal with even a relatively minor case like ours.
The downside to this sort of generosity of the benefit of the doubt, of course, is that then there are people who can't hack it and who create more shelter dogs. I don't have a good solution for that, of course. But my intuition is more good is created than bad.
[0] - His pathfinding is just not good. He'll go the entire way around the house to avoid walking over a scary black tape line. He'll also squeeze under tables, chairs, benches, etc. to avoid innocuous spaces or hop over the couch to avoid going around it. And this dog is a mess of Labrador, Staffordshire, and German Shepherd, with legs like a greyhound--watching him accordion on down to squeeze under a foot-high bench is hilarious.