When I was growing up we only ever ate "open face" sandwiches. Possibly because in Europe we use superior rye bread, which is denser and more filling than the white fluffy stuff that passes for bread here in north america. Also possibly because we were poor, and who wants to waste bread by doubling up a sandwich? Most of the flavour is in the toppings anyway.
So I don't really know if the main purpose of sandwiches is to eat lazily. With open face sandwiches (aka sandwiches) you can't just grab it in any way you want - you have to make sure you don't get any butter or mustard on your fingers.
I see a lot of people here on this continent being snobby about the open face sandwich. It's not right.