I understand the point and am sympathetic to it, but I'm just a bit cautious putting that into practise. Identity is a tricky thing and tightly defining it like that isn't often easy. A lot of immigrants saw assimilation as the peak goal so that their children wouldn't face the racism they did, so some of the latching onto identity is a form of resisting that racism from some people. Further, some oppressed minorities that fit into your definitions; for example, African Americans who still identify strongly with West African or Caribbean connections that fit your description but, due to their non-whiteness, wouldn't be considered fully American for most of America's history.

Again, not to say you aren't correct, but that identity is really slippery and the material reasons for why Americans are that way can make some sense in historical context.