You can see the difference between one immediate family and another in the DNA. DNA differences range from distinctions between individuals to distinctions between species. How do you decide where it makes sense to draw a middle line and say "ethnic group"?

One thing that you definitely can't trace in the DNA is "that group of people tried to genocide my grandparents", but that seems like an important "ethnic group" distinction to you.

This is not to dispute your main point which I take to be that you stop fighting over "ethnic" distinctions by giving people a new unifying identity, but I still find myself thinking that something is lost in the process, even if it is a proven approach.