Look, I find ancestry/geneaology as fascinating as the next guy, but I am not "nearly half-Irish ethnically"or whatever just because three of my mom's grandparents were descended from 19th century Potato Famine refugees.
I am American. My parents were Americans. My grandparents, all Americans. My great-grandparents were Americans as well. Ok, I think I had a few great-great grandparents who were born in Switzerland on my paternal side....
The relevant part of my ancestry is that they were all light-skinned Europeans.
Using American as an ethnic label will always be impossible for obvious reasons. It will imply that old stock white & Christian Americans are somehow more American than descendants of other more recent immigrant groups.
But I agree that there is de facto an ethnic group that is (white) American. If you look at the status in the US in the 60s - the decade with the highest share of native born Americans - the majority of Americans of Northern and Western European descent had clearly merged into one common ethnc group regardless of ancestry by most valid definitions of ethnicity.
It just seems there lack a name for this as European American is associated with far right/supremacist groups and includes groups with a strong separate ethnic identity. White American is neutral, but even broader and - again - includes groups with a specific ethnic identity (like Jews). WASP is incorrect as several Catholic and/or non-British groups are in the ethnically American group.