Now that you said this... this makes sense to me. I think I follow this... but hardly cook hot sandwiches myself.
It wouldn't even occur to me to cut in half equally LOL. I have always been diagonal, I think it makes more sense, easier to get that first bite in on the edge
I'm a nice boring A rectangle girl - I used to do diagonals and not really sure when and why it changed.
Even when I cut it in half, my tomato always seems to fall apart and slide down my forearm. I'm a little funny about stuff like that, so I end up using about a gazillion napkins and feel like I need a shower after the burger eating is done. LOL