Why do most sandwich makers have a triangular shape?
Typically with these sandwiches you have some cheese inside along with some other ingredients such as tomatoes that get quite hot (325° F sometimes).

From what I've seen, if you have a square only shape, you don't necessarily get a good seal, plus you get a massive pocket of hot lava.  The fat from the cheese or butter concentrates in the center, soaks and can break through the bread releasing hot lava on shirts, pants, open toes, etc.

Even if it doesn't suffer a total failure, you don't get a consistent sandwich.  Center will end up much soggier than the crusty rim and eating it can get difficult and messy.  Certainly no longer hors d'oeuvres stuff. 

The triangular shape essentially makes it bite-sized, so the stuffing doesn't run away after the first bite and becomes more manageable.

You can try using a grill or a panini press, but if you've noticed, those ones allow the oozing lava to escape and run away.  A calzone is similar to what you'd get, and a badly crafted calzone can be quite messy and again, not really an hors d'oeuvre.