Here you quite often did see people with dogs on a lead in department stores, it is not so common now, as most people nip into shops on the way to or from work, not when they are walking the dog.
Here in Denmark, dogs and other pets are not allowed in any shop that sells food, or in cafés or restaurants that serve food, nor in a chemist's.
I agree most dogs don't enjoy being taken into crowded places, which should rule most shops out. Unfortunately the usual solutions of shops having pegs outside that you could tether a dog lead to has fallen into disuse as dogs have been stolen from them!
I personally wouldn't take a dog into a store, but I don't mind if others do, as long as the dog is well-trained.
Obviously this is a problem for those who are afraid of dogs, and as fears are irrational, I don't think the onus is entirely on the person who doesn't care for dogs to avoid them. As a pet owner I feel obliged to consider other people when out with my pet.