Moreover, I don't even know what you mean by "roots." The US is a country of immigrants. What qualifies as having "American roots" in your view?
Well you used a word that is crucial imho, roots, means where you come from, origins. I feel like I tend to have libertarian views regarding choosing your identity, which includes calling yourself American, Austrian or whatever, ultimately it’s you that should make this decision. But just adding hyphens to people with historical significance that decided to move to a country that at the time gave them an economic incentive by having the best market feels dirty. Especially considering that most other countries don’t do this.