“Citizenship”, an outdated word?

I think “citizenship” is an outdated word. Same as “citizen”. Because it comes from the word ‘city”. Back in the old days, we had no countries, but more like giant city states with land around them. So, a member of a society there was called a “citizen”, and he had “citizenship”. Now, we have had nation-states for a long time, also known as “countries”. Therefore, a person who is a legal member of a country should be called a “countrizen” and have a “countrizenship”. It just seems so much more correct. The people of the Vatican and Singapore and other such small city states are the only ones that should have “citizenship”.