Hmmm, interesting point. I wonder if it really matters. I put that there only so they know I'm a U.S. citizen and hence have legal right to work there. Can you suggest a succinct alternative?
"Authorized to work in the United States." Yes, I am a lawyer, and I used to practice immigration law.
Saying you're eligible to work somewhere is different than disclosing your nationality. One is a material part of the hiring process; the other is something people discriminate on.
Stick to the things that actually affect job performance. It keeps the process fair for everyone.