I mean the type where mustard is placed on the hot griddle, and the patty is placed or smashed on top.
Mustard is actually mostly water (with some vinegar and mustard powder mixed in). The water inhibits browning of the patty and causes the patty to be steamed, so it does not seem like a great idea to put it below the patty.
There are other ways to add mustard flavor to the burger, like adding mustard or mustard powder to the sauce, or smearing mustard or mustard powder on the patty after it has been cooked. You could even season the patty with mustard powder before cooking it.
So, why place the patty on that mix of water, vinegar and mustard powder, which we know as mustard?