For people that have been here many generations, it's the only logical answer for ethnicity on the census form. My dad's family is Scotch-Irish with some Cherokee thrown in. My mom's family is German. What am I supposed to select if given a list of European nationalities? The only sensible selection is "white American". Now throw on top of it I have a couple kids and I have no idea really what my wife's family are beyond "white American" when that is half my kids genetically. You also have people that only follow ethnicity paternally because that's where their surname comes from, so they can make a selection but the selection is probably wrong.
"Scotch-Irish" is a term that's meaningless outside America anyway*, so I'm not convinced that "American" isn't a better designator.
A very few Ulster Protestants will identify as Ulster Scots, but it's a minority pursuit and none of them will use the term 'Scotch-Irish', nor is there very much in common culturally between Ballymena and Appalachia.
No one here uses Ulster Scots. If forced to select something European with a gun to my head, I'd say Scotch-Irish.