Surely 'ethnic americans' are Native North Americans?
This is the thing. Ethnicity gets wrapped up in a value judgement. We don't want to talk about ethnic Americans, but are willing to talk about ethnic Britons. Which then implies some rights those ethnic groups should have. But I would dare say the majority of 'ethnic Britons' wouldn't identify as British.
So I'd rather not use it in a way that conflates nationhood with ethnicity.