However, they are ridiculously common in the US hunter ring over fences as no more than a fashion accessory.
And yes, they are more common in the American hunt field, at least in my area, than running martingales.
As far as the OP's pony, the martingale is not restricting her head and neck over fences at all. As far as head carriage or head set, there's nothing really terribly wrong either. What could be improved is the way the pony uses herself. If she carried herself in better balance and pushed from behind rather than towing herself along on her front end, she's carry a better topline.
That flatwork would carry over to over fences as well, so she might engage evenly behind and round over her fences, rather than cantering over in a long flat stride.