One advantage I see to the border edges being visible is that it can inform the player where the spawn points are (if any). In the Smash TV screenshot, it shows the doors where the enemies come from. But without the borders, the player doesn't know if they should be anticipating attacks from just one direction or all directions.
Viewing post in Screen estate versus aestetics
Good point. I didn't even think of the practical implications. Also, you can place GUI elements outside of the arena, so it don't obscures the action.
If the borders were a part of the gameplay, something physical you can bumb into, then it makes sense to let it be a visible in-game element rather than just the monitor edge.
I tried splitting Resistance is Fruitile up, so that the play area is to the left, with the non-playarea stuff marked with red. It really take up alot of screen area! Might be worth it, but it's really a bold design decision.