Is it a known technique to serve hot crispy-crust sandwiches on edge? So, I'm not a chef and there are few foods I'm good at cooking. Grilled sandwiches, however, I would say are one of these few. Of course, for such sandwiches, with grilled or toasted bread, the crispness of the bread from toasting or grilling is a major component of the food experience. However, I have found that serving a sandwich the standard way, with on bread slice down, often results in a severe reduction in crispness, especially if the sandwich contains meat or other juicy items. Even if the sandwich insides are not so juicy, like for a grilled cheese, the release of water vapor due to the fact that the sandwich is hot, and having it trapped there between the sandwich and the plate, is enough to completely nullify the crispness of that piece of bread.

My personal solution to this is to cut the sandwich, typically diagonally, and plate it with the cut side down, so as to allow the release of water vapor to the air, and to mitigate juices going straight to the bread. I have found this to work quite well, as long as the sandwich is one that basically holds itself together decently well. (a toothpick can help.)

My question is whether this is a known plating technique for sandwiches, where the purpose of such plating is to maintain bread texture properties.
I think this is a perfectly legitimate question. Flat plating of a grilled sandwich will almost always result in the bottom piece of bread being steamed by the time it is eaten. Grilling with thicker or denser bread somewhat alleviates the problem, as well as grilling with a roll sliced and grilled on the cut side. 

As for presentation, your method is definitely not unheard of. The comment about the Club Sandwich is point on. You might also consider serving your sandwich with one half of the sandwich laying against some chips or veggie slices (carrot or celery sticks). That would keep the steam from developing under the sandwich. Then place the second half on the plate, barely overlapping the first. Grilled sandwiches are just one of those things that don't hold too long for service.