Of course, but many sandwiches are served on rolls. The question is what sandwich is the archetype. The example sandwich you envision when someone says the word "sandwich".
Let's say you asked a business associate to grab you a sandwich while he was going out, and let's assume there was no time to specify your type preference. What sort of sandwich would you expect to receive?
I would imagine you would expect to receive some sort of cold sandwich on long roll or between two slices of bread. It would consist of meat cheese and various vegetables with possibly mayo or mustard.
If you received a burger or a grilled cheese sandwich you'd be pretty surprised. In the burger case you would probably note that if you wanted a burger you would have asked for a burger not a sandwich.
Another way to put this might be there's really two definitions of sandwiches. There's a technical definition, but then there's another definition based on categorizing lunches into simple descriptions. Going out for sandwiches is not the same as going out for burgers. This is useful because we have joints that specialize in sandwiches that aren't burgers (and typically most menu items are cold sandwiches), and burger joints.