It's been four generations since we've had substantial European immigration. In most cases the various European groups are so thoroughly interbred that there's not much case for classifying them individually.
Thats what I thought about when I read the question. Especially the older northern and western European groups have basically lost their identity and become WASPs. I have relatives in the US that are of 25-50% Danish origin, but none of them consider themselves Danish-Americans. A label like Scottish-American is obviously even more meaningless.