I just became a US citizen after living in the country for 23 years. For me, the notion isn't archaic at all. I was a permanent resident for some time. The US could revoke my residency if I spent more than six months consecutively outside the USA.
I do think many people think the term is becoming archaic. For people who live and call a country which they are not citizen in their home, it's definitely not archaic. Becoming a US citizen was one of the most important days of my life.